Communication

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Abacus school

Abacus or abaco refers to calculations, especially the subject of direct calculations, using Hindu numerals without the help of the abacus (an instrument for calculating).

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Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī

Abū al-Ḥasan ibn ʿAlī ibn Muḥammad ibn ʿAlī al-Qalaṣādī (1412–1486) was a Muslim Arab mathematician from Al-Andalus specializing in Islamic inheritance jurisprudence.

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Abū Kāmil Shujāʿ ibn Aslam

(Latinized as Auoquamel, ابو كامل, also known as al-ḥāsib al-miṣrī—lit. "the Egyptian reckoner") (c. 850 – c. 930) was an Egyptian Muslim mathematician during the Islamic Golden Age.

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Abel–Ruffini theorem

In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no algebraic solution—that is, solution in radicals—to the general polynomial equations of degree five or higher with arbitrary coefficients.

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Abraham Robinson

Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics.

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Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

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Abu al-Wafa' Buzjani

Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī (ابوالوفا بوزجانی or بوژگانی) (10 June 940 – 15 July 998) was a Persian mathematician and astronomer who worked in Baghdad.

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Accounting

Accounting or accountancy is the measurement, processing, and communication of financial information about economic entities such as businesses and corporations.

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Addison-Wesley

Addison-Wesley is a publisher of textbooks and computer literature.

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Adelard of Bath

Adelard of Bath (Adelardus Bathensis; 1080 1152 AD) was a 12th-century English natural philosopher.

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Adolph P. Yushkevich

Adolph-Andrei Pavlovich Yushkevich (Адо́льф-Андре́й Па́влович Юшке́вич; 15 July 1906 – 17 July 1993) was a Soviet historian of mathematics, leading expert in medieval mathematics of the East and the work of Leonhard Euler.

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Akkad (region)

Akkad is the historical name of a region in northern Mesopotamia around the city of Akkad, probably near the confluence of the Diyala with the Tigris.

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Al-Biruni

Abū Rayḥān Muḥammad ibn Aḥmad Al-Bīrūnī (Chorasmian/ابوریحان بیرونی Abū Rayḥān Bērōnī; New Persian: Abū Rayḥān Bīrūnī) (973–1050), known as Al-Biruni (البيروني) in English, was an IranianD.J. Boilot, "Al-Biruni (Beruni), Abu'l Rayhan Muhammad b. Ahmad", in Encyclopaedia of Islam (Leiden), New Ed., vol.1:1236–1238.

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Al-Karaji

(c. 953 – c. 1029) was a 10th-century Persian mathematician and engineer who flourished at Baghdad.

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Al-Kindi

Abu Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; Alkindus; c. 801–873 AD) was an Arab Muslim philosopher, polymath, mathematician, physician and musician.

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Alan Turing

Alan Mathison Turing (23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist.

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Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

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Alexander Grothendieck

Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.

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Alexander Marshack

Alexander Marshack (April 4, 1918 – December 20, 2004) was an American independent scholar and Paleolithic archaeologist.

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Alexander the Great

Alexander III of Macedon (20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great (Aléxandros ho Mégas), was a king (basileus) of the ancient Greek kingdom of Macedon and a member of the Argead dynasty.

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Alexandria

Alexandria (or; Arabic: الإسكندرية; Egyptian Arabic: إسكندرية; Ⲁⲗⲉⲝⲁⲛⲇⲣⲓⲁ; Ⲣⲁⲕⲟⲧⲉ) is the second-largest city in Egypt and a major economic centre, extending about along the coast of the Mediterranean Sea in the north central part of the country.

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Alfred North Whitehead

Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.

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Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

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Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.

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Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

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Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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Algeria

Algeria (الجزائر, familary Algerian Arabic الدزاير; ⴷⵣⴰⵢⴻⵔ; Dzayer; Algérie), officially the People's Democratic Republic of Algeria, is a sovereign state in North Africa on the Mediterranean coast.

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Algorism

Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits.

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Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Almagest

The Almagest is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy. One of the most influential scientific texts of all time, its geocentric model was accepted for more than 1200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Analytic geometry

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

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Ancient Egypt

Ancient Egypt was a civilization of ancient Northeastern Africa, concentrated along the lower reaches of the Nile River - geographically Lower Egypt and Upper Egypt, in the place that is now occupied by the countries of Egypt and Sudan.

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Ancient Egyptian mathematics

Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c. 300 BC, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt.

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Ancient Roman architecture

Ancient Roman architecture adopted the external language of classical Greek architecture for the purposes of the ancient Romans, but differed from Greek buildings, becoming a new architectural style.

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Ancient Rome

In historiography, ancient Rome is Roman civilization from the founding of the city of Rome in the 8th century BC to the collapse of the Western Roman Empire in the 5th century AD, encompassing the Roman Kingdom, Roman Republic and Roman Empire until the fall of the western empire.

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André Weil

André Weil (6 May 1906 – 6 August 1998) was an influential French mathematician of the 20th century, known for his foundational work in number theory, algebraic geometry.

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Andrew Wiles

Sir Andrew John Wiles (born 11 April 1953) is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory.

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Andrey Kolmogorov

Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a 20th-century Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.

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Angle trisection

Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.

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Anthemius of Tralles

Anthemius of Tralles (Ἀνθέμιος ὁ Τραλλιανός, Medieval Greek:, Anthémios o Trallianós; – 533 558) was a Greek from Tralles who worked as a geometer and architect in Constantinople, the capital of the Byzantine Empire.

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Antikythera mechanism

The Antikythera mechanism is an ancient Greek analogue computer and orrery used to predict astronomical positions and eclipses for calendar and astrological purposes decades in advance.

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Apollonius of Perga

Apollonius of Perga (Ἀπολλώνιος ὁ Περγαῖος; Apollonius Pergaeus; late 3rdearly 2nd centuries BC) was a Greek geometer and astronomer known for his theories on the topic of conic sections.

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Applied mathematics

Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry.

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Arabic

Arabic (العَرَبِيَّة) or (عَرَبِيّ) or) is a Central Semitic language that first emerged in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. It is named after the Arabs, a term initially used to describe peoples living from Mesopotamia in the east to the Anti-Lebanon mountains in the west, in northwestern Arabia, and in the Sinai peninsula. Arabic is classified as a macrolanguage comprising 30 modern varieties, including its standard form, Modern Standard Arabic, which is derived from Classical Arabic. As the modern written language, Modern Standard Arabic is widely taught in schools and universities, and is used to varying degrees in workplaces, government, and the media. The two formal varieties are grouped together as Literary Arabic (fuṣḥā), which is the official language of 26 states and the liturgical language of Islam. Modern Standard Arabic largely follows the grammatical standards of Classical Arabic and uses much of the same vocabulary. However, it has discarded some grammatical constructions and vocabulary that no longer have any counterpart in the spoken varieties, and has adopted certain new constructions and vocabulary from the spoken varieties. Much of the new vocabulary is used to denote concepts that have arisen in the post-classical era, especially in modern times. During the Middle Ages, Literary Arabic was a major vehicle of culture in Europe, especially in science, mathematics and philosophy. As a result, many European languages have also borrowed many words from it. Arabic influence, mainly in vocabulary, is seen in European languages, mainly Spanish and to a lesser extent Portuguese, Valencian and Catalan, owing to both the proximity of Christian European and Muslim Arab civilizations and 800 years of Arabic culture and language in the Iberian Peninsula, referred to in Arabic as al-Andalus. Sicilian has about 500 Arabic words as result of Sicily being progressively conquered by Arabs from North Africa, from the mid 9th to mid 10th centuries. Many of these words relate to agriculture and related activities (Hull and Ruffino). Balkan languages, including Greek and Bulgarian, have also acquired a significant number of Arabic words through contact with Ottoman Turkish. Arabic has influenced many languages around the globe throughout its history. Some of the most influenced languages are Persian, Turkish, Spanish, Urdu, Kashmiri, Kurdish, Bosnian, Kazakh, Bengali, Hindi, Malay, Maldivian, Indonesian, Pashto, Punjabi, Tagalog, Sindhi, and Hausa, and some languages in parts of Africa. Conversely, Arabic has borrowed words from other languages, including Greek and Persian in medieval times, and contemporary European languages such as English and French in modern times. Classical Arabic is the liturgical language of 1.8 billion Muslims and Modern Standard Arabic is one of six official languages of the United Nations. All varieties of Arabic combined are spoken by perhaps as many as 422 million speakers (native and non-native) in the Arab world, making it the fifth most spoken language in the world. Arabic is written with the Arabic alphabet, which is an abjad script and is written from right to left, although the spoken varieties are sometimes written in ASCII Latin from left to right with no standardized orthography.

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Arabic numerals

Arabic numerals, also called Hindu–Arabic numerals, are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, based on the Hindu–Arabic numeral system, the most common system for the symbolic representation of numbers in the world today.

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Arabs

Arabs (عَرَب ISO 233, Arabic pronunciation) are a population inhabiting the Arab world.

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Archimedean spiral

The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd century BC Greek mathematician Archimedes.

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Archimedes

Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

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Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

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Aristotle

Aristotle (Ἀριστοτέλης Aristotélēs,; 384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece.

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Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

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Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

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Arithmetic progression

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

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Arnaldus de Villa Nova

Arnaldus de Villa Nova (also called Arnau de Vilanova in Valencian, his language, Arnaldus Villanovanus, Arnaud de Ville-Neuve or Arnaldo de Villanueva, c. 1240–1311) was a physician and a religious reformer.

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Ars Magna (Gerolamo Cardano)

The Ars Magna ("The Great Art") is an important Latin-language book on algebra written by Girolamo Cardano.

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Artifact (archaeology)

An artifact, or artefact (see American and British English spelling differences), is something made or given shape by humans, such as a tool or a work of art, especially an object of archaeological interest.

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ArXiv

arXiv (pronounced "archive") is a repository of electronic preprints (known as e-prints) approved for publication after moderation, that consists of scientific papers in the fields of mathematics, physics, astronomy, computer science, quantitative biology, statistics, and quantitative finance, which can be accessed online.

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Aryabhata

Aryabhata (IAST) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.

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Aryabhatiya

Aryabhatiya (IAST) or Aryabhatiyam, a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata.

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Assyria

Assyria, also called the Assyrian Empire, was a major Semitic speaking Mesopotamian kingdom and empire of the ancient Near East and the Levant.

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Astronomy

Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.

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Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.

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Athens

Athens (Αθήνα, Athína; Ἀθῆναι, Athênai) is the capital and largest city of Greece.

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Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.

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Autodidacticism

Autodidacticism (also autodidactism) or self-education (also self-learning and self-teaching) is education without the guidance of masters (such as teachers and professors) or institutions (such as schools).

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Axiomatic system

In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.

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Évariste Galois

Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.

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Babylon

Babylon (KA2.DIĜIR.RAKI Bābili(m); Aramaic: בבל, Babel; بَابِل, Bābil; בָּבֶל, Bavel; ܒܒܠ, Bāwēl) was a key kingdom in ancient Mesopotamia from the 18th to 6th centuries BC.

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Babylonia

Babylonia was an ancient Akkadian-speaking state and cultural area based in central-southern Mesopotamia (present-day Iraq).

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Babylonian mathematics

Babylonian mathematics (also known as Assyro-Babylonian mathematics) was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC.

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Baghdad

Baghdad (بغداد) is the capital of Iraq.

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Bartel Leendert van der Waerden

Bartel Leendert van der Waerden (February 2, 1903 – January 12, 1996) was a Dutch mathematician and historian of mathematics.

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Bartholomaeus Pitiscus

Bartholomaeus Pitiscus (also Barthélemy, Bartholomeo, August 24, 1561 – July 2, 1613) was a 16th-century German trigonometrist, astronomer and theologian who first coined the word trigonometry.

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Béjaïa

Béjaïa (بِجَايَة, Bijayah; Bgayet, Bgayeth, ⴱⴳⴰⵢⴻⵜ), formerly Bougie and Bugia, is a Mediterranean port city on the Gulf of Béjaïa in Algeria; it is the capital of Béjaïa Province, Kabylia.

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BBC

The British Broadcasting Corporation (BBC) is a British public service broadcaster.

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Benoit Mandelbrot

Benoit B.  Mandelbrot  (20 November 1924 – 14 October 2010) was a Polish-born, French and American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life".

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Berlin Papyrus 6619

The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear, is an ancient Egyptian papyrus document from the Middle Kingdom, second half of the 12th or 13th dynasty.

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Bernhard Riemann

Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.

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Bertrand Russell

Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.

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Bhāskara II

Bhāskara (also known as Bhāskarāchārya ("Bhāskara, the teacher"), and as Bhaskara II to avoid confusion with Bhāskara I) (1114–1185), was an Indian mathematician and astronomer.

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Bible

The Bible (from Koine Greek τὰ βιβλία, tà biblía, "the books") is a collection of sacred texts or scriptures that Jews and Christians consider to be a product of divine inspiration and a record of the relationship between God and humans.

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Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

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Binomial theorem

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

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Blaise Pascal

Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Catholic theologian.

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Boethius

Anicius Manlius Severinus Boëthius, commonly called Boethius (also Boetius; 477–524 AD), was a Roman senator, consul, magister officiorum, and philosopher of the early 6th century.

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Book of Wisdom

The Wisdom of Solomon or Book of Wisdom is a Jewish work, written in Greek, composed in Alexandria (Egypt).

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Bookkeeping

Bookkeeping is the recording of financial transactions, and is part of the process of accounting in business.

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Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

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Brahmagupta

Brahmagupta (born, died) was an Indian mathematician and astronomer.

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Brahmagupta theorem

In geometry, Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.

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Brahmagupta's formula

In Euclidean geometry, Brahmagupta's formula is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides.

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Brahmagupta's identity

In algebra, Brahmagupta's identity says that the product of two numbers of the form a^2+nb^2 is itself a number of that form.

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Brahmi numerals

The Brahmi numerals are a numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens).

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Brāhmasphuṭasiddhānta

The Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is the main work of Brahmagupta, written c. 628.

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British Museum

The British Museum, located in the Bloomsbury area of London, United Kingdom, is a public institution dedicated to human history, art and culture.

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Burning of books and burying of scholars

The burning of books and burying of scholars refers to the supposed burning of texts in 213 BCE and live burial of 460 Confucian scholars in 212 BCE by the First Emperor of the Qin dynasty of ancient China.

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Byzantine Empire

The Byzantine Empire, also referred to as the Eastern Roman Empire and Byzantium, was the continuation of the Roman Empire in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinople (modern-day Istanbul, which had been founded as Byzantium).

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Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Calendar

A calendar is a system of organizing days for social, religious, commercial or administrative purposes.

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Calendar reform

Calendar reform, properly calendrical reform, is any significant revision of a calendar system.

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Caliphate

A caliphate (خِلافة) is a state under the leadership of an Islamic steward with the title of caliph (خَليفة), a person considered a religious successor to the Islamic prophet Muhammad and a leader of the entire ummah (community).

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Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Catastrophe theory

In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.

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Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

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Cavalieri's principle

In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows.

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Celestial mechanics

Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects.

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Central America

Central America (América Central, Centroamérica) is the southernmost, isthmian portion of the North American continent, which connects with the South American continent on the southeast.

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Central Asia

Central Asia stretches from the Caspian Sea in the west to China in the east and from Afghanistan in the south to Russia in the north.

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Central Italy

Central Italy (Italia centrale or just Centro) is one of the five official statistical regions of Italy used by the National Institute of Statistics (ISTAT), a first level NUTS region and a European Parliament constituency.

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Chữ Nôm

Chữ Nôm (literally "Southern characters"), in earlier times also called quốc âm or chữ nam, is a logographic writing system formerly used to write the Vietnamese language.

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Chinese characters

Chinese characters are logograms primarily used in the writing of Chinese and Japanese.

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Chinese mathematics

Mathematics in China emerged independently by the 11th century BC.

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Chinese pagoda

Chinese pagodas are a traditional part of Chinese architecture.

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Christianity

ChristianityFrom Ancient Greek Χριστός Khristós (Latinized as Christus), translating Hebrew מָשִׁיחַ, Māšîăḥ, meaning "the anointed one", with the Latin suffixes -ian and -itas.

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Cicero

Marcus Tullius Cicero (3 January 106 BC – 7 December 43 BC) was a Roman statesman, orator, lawyer and philosopher, who served as consul in the year 63 BC.

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Circle

A circle is a simple closed shape.

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Circolo Matematico di Palermo

The Circolo Matematico di Palermo (Mathematical Circle of Palermo) is an Italian mathematical society, founded in Palermo by Sicilian geometer Giovanni B. Guccia in 1884.

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Circumference

In geometry, the circumference (from Latin circumferentia, meaning "carrying around") of a circle is the (linear) distance around it.

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Classification of finite simple groups

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four broad classes described below.

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Claude Shannon

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory".

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Clay Mathematics Institute

The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.

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Combinatorial game theory

Combinatorial game theory (CGT) is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information.

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Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

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Commodus

Commodus (31 August 161– 31 December 192AD), born Lucius Aurelius Commodus and died Lucius Aelius Aurelius Commodus, was Roman emperor with his father Marcus Aurelius from177 to his father's death in 180, and solely until 192.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Composite number

A composite number is a positive integer that can be formed by multiplying together two smaller positive integers.

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Compound interest

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.

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Computability theory

Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.

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Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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Computer

A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

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Computer algebra

In computational mathematics, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Configuration (geometry)

In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.

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Confucianism

Confucianism, also known as Ruism, is described as tradition, a philosophy, a religion, a humanistic or rationalistic religion, a way of governing, or simply a way of life.

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Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Continuum hypothesis

In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.

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Control theory

Control theory in control systems engineering deals with the control of continuously operating dynamical systems in engineered processes and machines.

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Counting rods

Counting rods are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia.

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Cryptanalysis

Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to loosen" or "to untie") is the study of analyzing information systems in order to study the hidden aspects of the systems.

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Cube (algebra)

In arithmetic and algebra, the cube of a number is its third power: the result of the number multiplied by itself twice: It is also the number multiplied by its square: This is also the volume formula for a geometric cube with sides of length, giving rise to the name.

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Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

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Cuneiform script

Cuneiform script, one of the earliest systems of writing, was invented by the Sumerians.

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Curve

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.

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Data analysis

Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making.

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David Hilbert

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.

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De Prospectiva Pingendi

De Prospectiva pingendi (On the Perspective of painting) is the earliest and only pre–1500 Renaissance treatise solely devoted to the subject of perspective.

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Decidability (logic)

In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a boolean true or false value that is correct (instead of looping indefinitely, crashing, returning "don't know" or returning a wrong answer).

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Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

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Decimal separator

A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form.

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Democratic Republic of the Congo

The Democratic Republic of the Congo (République démocratique du Congo), also known as DR Congo, the DRC, Congo-Kinshasa or simply the Congo, is a country located in Central Africa.

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Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Derrick Henry Lehmer

Derrick Henry "Dick" Lehmer (February 23, 1905 – May 22, 1991) was an American mathematician who refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes.

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Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

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Differential calculus

In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.

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Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Diophantine approximation

In number theory, the field of Diophantine approximation deals with the approximation of real numbers by rational numbers.

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Diophantine equation

In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).

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Diophantus

Diophantus of Alexandria (Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died around 84 years old, probably sometime between AD 285 and 299) was an Alexandrian Hellenistic mathematician, who was the author of a series of books called Arithmetica, many of which are now lost.

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Dirk Jan Struik

Dirk Jan Struik (September 30, 1894 – October 21, 2000) was a Dutch mathematician, historian of mathematics and Marxian theoretician who spent most of his life in the United States.

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Discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

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Distance

Distance is a numerical measurement of how far apart objects are.

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Distribution (mathematics)

Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.

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Divergent series

In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

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Division (mathematics)

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

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Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.

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Dynamical systems theory

Dynamical systems theory is an area of mathematics used to describe the behavior of the complex dynamical systems, usually by employing differential equations or difference equations.

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East Asian cultural sphere

The "Sinosphere", or "East Asian cultural sphere", refers to a grouping of countries and regions in East Asia that were historically influenced by the Chinese culture.

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Ebla

Ebla (إبلا., modern: تل مرديخ, Tell Mardikh) was one of the earliest kingdoms in Syria.

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Edinburgh Mathematical Society

The Edinburgh Mathematical Society is a mathematical society for academics in Scotland.

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Egypt

Egypt (مِصر, مَصر, Khēmi), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and southwest corner of Asia by a land bridge formed by the Sinai Peninsula.

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Egyptian language

The Egyptian language was spoken in ancient Egypt and was a branch of the Afro-Asiatic languages.

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Egyptians

Egyptians (مَصريين;; مِصريّون; Ni/rem/en/kīmi) are an ethnic group native to Egypt and the citizens of that country sharing a common culture and a common dialect known as Egyptian Arabic.

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Elementary algebra

Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.

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Ellipse

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

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Elliptic geometry

Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.

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Emmy Noether

Amalie Emmy NoetherEmmy is the Rufname, the second of two official given names, intended for daily use.

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England

England is a country that is part of the United Kingdom.

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ENIAC

ENIAC (Electronic Numerical Integrator and Computer) was amongst the earliest electronic general-purpose computers made.

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Eratosthenes

Eratosthenes of Cyrene (Ἐρατοσθένης ὁ Κυρηναῖος,; –) was a Greek mathematician, geographer, poet, astronomer, and music theorist.

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Erdős number

The Erdős number describes the "collaborative distance" between mathematician and another person, as measured by authorship of mathematical papers.

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Ergodic theory

Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems.

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Error correction code

In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels.

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Etruscan civilization

The Etruscan civilization is the modern name given to a powerful and wealthy civilization of ancient Italy in the area corresponding roughly to Tuscany, western Umbria and northern Lazio.

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Etruscan numerals

The Etruscan numerals were used by the ancient Etruscans.

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Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

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Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

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Eudoxus of Cnidus

Eudoxus of Cnidus (Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato.

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Eutocius of Ascalon

Eutocius of Ascalon (Εὐτόκιος ὁ Ἀσκαλωνίτης; 480 – 540) was a Greek mathematician who wrote commentaries on several Archimedean treatises and on the Apollonian Conics.

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Exponential growth

Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.

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Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

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Fast Fourier transform

A fast Fourier transform (FFT) is an algorithm that samples a signal over a period of time (or space) and divides it into its frequency components.

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February 29

February 29, also known as leap day or leap year day, is a date added to most years that are divisible by 4, such as 2008, 2012, 2016, 2020, and 2024.

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Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.

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Fibonacci

Fibonacci (c. 1175 – c. 1250) was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".

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Fibonacci number

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: Often, especially in modern usage, the sequence is extended by one more initial term: By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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Fixed-point theorem

In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x).

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Flanders

Flanders (Vlaanderen, Flandre, Flandern) is the Dutch-speaking northern portion of Belgium, although there are several overlapping definitions, including ones related to culture, language, politics and history.

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Foundations of mathematics

Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.

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Four color theorem

In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.

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Fractal

In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.

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Fraud

In law, fraud is deliberate deception to secure unfair or unlawful gain, or to deprive a victim of a legal right.

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Frequency analysis

In cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a ciphertext.

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Frustum

In geometry, a frustum (plural: frusta or frustums) is the portion of a solid (normally a cone or pyramid) that lies between one or two parallel planes cutting it.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Functional analysis

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.

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Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

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Galileo Galilei

Galileo Galilei (15 February 1564Drake (1978, p. 1). The date of Galileo's birth is given according to the Julian calendar, which was then in force throughout Christendom. In 1582 it was replaced in Italy and several other Catholic countries with the Gregorian calendar. Unless otherwise indicated, dates in this article are given according to the Gregorian calendar. – 8 January 1642) was an Italian polymath.

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Gambling

Gambling is the wagering of money or something of value (referred to as "the stakes") on an event with an uncertain outcome with the primary intent of winning money or material goods.

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Game theory

Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".

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Gamma function

In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.

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Gaussian elimination

In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.

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Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.

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Gear

A gear or cogwheel is a rotating machine part having cut like teeth, or cogs, which mesh with another toothed part to transmit torque.

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General hypergeometric function

In mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the hypergeometric function that was introduced by.

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General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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Geometric mean

In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).

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Geometric series

In mathematics, a geometric series is a series with a constant ratio between successive terms.

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Geometric transformation

A geometric transformation is any bijection of a set having some geometric structure to itself or another such set.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.

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George Boole

George Boole (2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland.

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Gerard of Cremona

Gerard of Cremona (Latin: Gerardus Cremonensis; c. 1114 – 1187) was an Italian translator of scientific books from Arabic into Latin.

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Germany

Germany (Deutschland), officially the Federal Republic of Germany (Bundesrepublik Deutschland), is a sovereign state in central-western Europe.

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Gerolamo Cardano

Gerolamo (or Girolamo, or Geronimo) Cardano (Jérôme Cardan; Hieronymus Cardanus; 24 September 1501 – 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler.

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Ghent University

Ghent University (Universiteit Gent, abbreviated as UGent) is a public research university located in Ghent, Belgium.

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Giovanni di Casali

Giovanni (or Johannes) di Casali (or da Casale; c. 1320 – after 1374) was a friar in the Franciscan Order, a natural philosopher and a theologian, author of works on theology and science, and a papal legate.

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Giuseppe Peano

Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist.

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Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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Greco-Roman world

The Greco-Roman world, Greco-Roman culture, or the term Greco-Roman; spelled Graeco-Roman in the United Kingdom and the Commonwealth), when used as an adjective, as understood by modern scholars and writers, refers to those geographical regions and countries that culturally (and so historically) were directly, long-term, and intimately influenced by the language, culture, government and religion of the ancient Greeks and Romans. It is also better known as the Classical Civilisation. In exact terms the area refers to the "Mediterranean world", the extensive tracts of land centered on the Mediterranean and Black Sea basins, the "swimming-pool and spa" of the Greeks and Romans, i.e. one wherein the cultural perceptions, ideas and sensitivities of these peoples were dominant. This process was aided by the universal adoption of Greek as the language of intellectual culture and commerce in the Eastern Mediterranean Sea, and of Latin as the tongue for public management and forensic advocacy, especially in the Western Mediterranean. Though the Greek and the Latin never became the native idioms of the rural peasants who composed the great majority of the empire's population, they were the languages of the urbanites and cosmopolitan elites, and the lingua franca, even if only as corrupt or multifarious dialects to those who lived within the large territories and populations outside the Macedonian settlements and the Roman colonies. All Roman citizens of note and accomplishment regardless of their ethnic extractions, spoke and wrote in Greek and/or Latin, such as the Roman jurist and Imperial chancellor Ulpian who was of Phoenician origin, the mathematician and geographer Claudius Ptolemy who was of Greco-Egyptian origin and the famous post-Constantinian thinkers John Chrysostom and Augustine who were of Syrian and Berber origins, respectively, and the historian Josephus Flavius who was of Jewish origin and spoke and wrote in Greek.

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Greek language

Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.

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Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

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Greek numerals

Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet.

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Greeks

The Greeks or Hellenes (Έλληνες, Éllines) are an ethnic group native to Greece, Cyprus, southern Albania, Italy, Turkey, Egypt and, to a lesser extent, other countries surrounding the Mediterranean Sea. They also form a significant diaspora, with Greek communities established around the world.. Greek colonies and communities have been historically established on the shores of the Mediterranean Sea and Black Sea, but the Greek people have always been centered on the Aegean and Ionian seas, where the Greek language has been spoken since the Bronze Age.. Until the early 20th century, Greeks were distributed between the Greek peninsula, the western coast of Asia Minor, the Black Sea coast, Cappadocia in central Anatolia, Egypt, the Balkans, Cyprus, and Constantinople. Many of these regions coincided to a large extent with the borders of the Byzantine Empire of the late 11th century and the Eastern Mediterranean areas of ancient Greek colonization. The cultural centers of the Greeks have included Athens, Thessalonica, Alexandria, Smyrna, and Constantinople at various periods. Most ethnic Greeks live nowadays within the borders of the modern Greek state and Cyprus. The Greek genocide and population exchange between Greece and Turkey nearly ended the three millennia-old Greek presence in Asia Minor. Other longstanding Greek populations can be found from southern Italy to the Caucasus and southern Russia and Ukraine and in the Greek diaspora communities in a number of other countries. Today, most Greeks are officially registered as members of the Greek Orthodox Church.CIA World Factbook on Greece: Greek Orthodox 98%, Greek Muslim 1.3%, other 0.7%. Greeks have greatly influenced and contributed to culture, arts, exploration, literature, philosophy, politics, architecture, music, mathematics, science and technology, business, cuisine, and sports, both historically and contemporarily.

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Gregorian calendar

The Gregorian calendar is the most widely used civil calendar in the world.

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Gregory's series

Gregory's series, also known as the Madhava–Gregory series or Leibniz's series, is an infinite Taylor series expansion of the inverse tangent function.

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Grigori Perelman

Grigori Yakovlevich Perelman (a; born 13 June 1966) is a Russian mathematician.

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Gromatici

Gromatici (from Latin groma or gruma, a surveyor's pole) or agrimensores was the name for land-surveyors amongst the ancient Romans.

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Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

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Gupta Empire

The Gupta Empire was an ancient Indian empire, existing from approximately 240 to 590 CE.

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Hagia Sophia

Hagia Sophia (from the Greek Αγία Σοφία,, "Holy Wisdom"; Sancta Sophia or Sancta Sapientia; Ayasofya) is a former Greek Orthodox Christian patriarchal basilica (church), later an Ottoman imperial mosque and now a museum (Ayasofya Müzesi) in Istanbul, Turkey.

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Halayudha

Halayudha (Sanskrit: हलायुध) was a 10th-century Indian mathematician who wrote the, a commentary on Pingala's Chandaḥśāstra.

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Han dynasty

The Han dynasty was the second imperial dynasty of China (206 BC–220 AD), preceded by the Qin dynasty (221–206 BC) and succeeded by the Three Kingdoms period (220–280 AD). Spanning over four centuries, the Han period is considered a golden age in Chinese history. To this day, China's majority ethnic group refers to themselves as the "Han Chinese" and the Chinese script is referred to as "Han characters". It was founded by the rebel leader Liu Bang, known posthumously as Emperor Gaozu of Han, and briefly interrupted by the Xin dynasty (9–23 AD) of the former regent Wang Mang. This interregnum separates the Han dynasty into two periods: the Western Han or Former Han (206 BC–9 AD) and the Eastern Han or Later Han (25–220 AD). The emperor was at the pinnacle of Han society. He presided over the Han government but shared power with both the nobility and appointed ministers who came largely from the scholarly gentry class. The Han Empire was divided into areas directly controlled by the central government using an innovation inherited from the Qin known as commanderies, and a number of semi-autonomous kingdoms. These kingdoms gradually lost all vestiges of their independence, particularly following the Rebellion of the Seven States. From the reign of Emperor Wu (r. 141–87 BC) onward, the Chinese court officially sponsored Confucianism in education and court politics, synthesized with the cosmology of later scholars such as Dong Zhongshu. This policy endured until the fall of the Qing dynasty in 1911 AD. The Han dynasty saw an age of economic prosperity and witnessed a significant growth of the money economy first established during the Zhou dynasty (c. 1050–256 BC). The coinage issued by the central government mint in 119 BC remained the standard coinage of China until the Tang dynasty (618–907 AD). The period saw a number of limited institutional innovations. To finance its military campaigns and the settlement of newly conquered frontier territories, the Han government nationalized the private salt and iron industries in 117 BC, but these government monopolies were repealed during the Eastern Han dynasty. Science and technology during the Han period saw significant advances, including the process of papermaking, the nautical steering ship rudder, the use of negative numbers in mathematics, the raised-relief map, the hydraulic-powered armillary sphere for astronomy, and a seismometer for measuring earthquakes employing an inverted pendulum. The Xiongnu, a nomadic steppe confederation, defeated the Han in 200 BC and forced the Han to submit as a de facto inferior partner, but continued their raids on the Han borders. Emperor Wu launched several military campaigns against them. The ultimate Han victory in these wars eventually forced the Xiongnu to accept vassal status as Han tributaries. These campaigns expanded Han sovereignty into the Tarim Basin of Central Asia, divided the Xiongnu into two separate confederations, and helped establish the vast trade network known as the Silk Road, which reached as far as the Mediterranean world. The territories north of Han's borders were quickly overrun by the nomadic Xianbei confederation. Emperor Wu also launched successful military expeditions in the south, annexing Nanyue in 111 BC and Dian in 109 BC, and in the Korean Peninsula where the Xuantu and Lelang Commanderies were established in 108 BC. After 92 AD, the palace eunuchs increasingly involved themselves in court politics, engaging in violent power struggles between the various consort clans of the empresses and empresses dowager, causing the Han's ultimate downfall. Imperial authority was also seriously challenged by large Daoist religious societies which instigated the Yellow Turban Rebellion and the Five Pecks of Rice Rebellion. Following the death of Emperor Ling (r. 168–189 AD), the palace eunuchs suffered wholesale massacre by military officers, allowing members of the aristocracy and military governors to become warlords and divide the empire. When Cao Pi, King of Wei, usurped the throne from Emperor Xian, the Han dynasty would eventually collapse and ceased to exist.

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Harmonic mean

In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means.

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Hellenistic period

The Hellenistic period covers the period of Mediterranean history between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire as signified by the Battle of Actium in 31 BC and the subsequent conquest of Ptolemaic Egypt the following year.

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Henri Poincaré

Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

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Herman of Carinthia

Herman of Carinthia (c. 1100 – c. 1160), also nicknamed Hermannus Dalmata ("the Dalmatian"), Sclavus ("the Slav") or Secundus ("the Second"), was an Istrian philosopher, astronomer, astrologer, mathematician, translator and author.

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Hermann Grassmann

Hermann Günther Grassmann (Graßmann; April 15, 1809 – September 26, 1877) was a German polymath, known in his day as a linguist and now also as a mathematician.

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Hero of Alexandria

Hero of Alexandria (ἭρωνGenitive: Ἥρωνος., Heron ho Alexandreus; also known as Heron of Alexandria; c. 10 AD – c. 70 AD) was a mathematician and engineer who was active in his native city of Alexandria, Roman Egypt.

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Heron's formula

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulae for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.

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Highly composite number

A highly composite number (or anti-prime) is a positive integer with more divisors than any smaller positive integer has.

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Hilbert's problems

Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.

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Hindu–Arabic numeral system

The Hindu–Arabic numeral systemDavid Eugene Smith and Louis Charles Karpinski,, 1911 (also called the Arabic numeral system or Hindu numeral system) is a positional decimal numeral system that is the most common system for the symbolic representation of numbers in the world.

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Hipparchus

Hipparchus of Nicaea (Ἵππαρχος, Hipparkhos) was a Greek astronomer, geographer, and mathematician.

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Historia Mathematica

Historia Mathematica: International Journal of History of Mathematics is an academic journal on the history of mathematics published by Elsevier.

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Historian

A historian is a person who studies and writes about the past, and is regarded as an authority on it.

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History of algebra

As a branch of mathematics, algebra emerged at the end of the 16th century in Europe, with the work of François Viète.

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History of astronomy

Astronomy is the oldest of the natural sciences, dating back to antiquity, with its origins in the religious, mythological, cosmological, calendrical, and astrological beliefs and practices of prehistory: vestiges of these are still found in astrology, a discipline long interwoven with public and governmental astronomy, and not completely disentangled from it until a few centuries ago in the Western World (see astrology and astronomy).

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History of calculus

Calculus, known in its early history as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series.

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History of combinatorics

The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies.

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History of geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships.

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History of India

The history of India includes the prehistoric settlements and societies in the Indian subcontinent; the advancement of civilisation from the Indus Valley Civilisation to the eventual blending of the Indo-Aryan culture to form the Vedic Civilisation; the rise of Hinduism, Jainism and Buddhism;Sanderson, Alexis (2009), "The Śaiva Age: The Rise and Dominance of Śaivism during the Early Medieval Period." In: Genesis and Development of Tantrism, edited by Shingo Einoo, Tokyo: Institute of Oriental Culture, University of Tokyo, 2009.

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History of logic

The history of logic deals with the study of the development of the science of valid inference (logic).

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History of mathematical notation

The history of mathematical notation includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness.

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History of statistics

The history of statistics in the modern sense dates from the mid-17th century, with the term statistics itself coined in 1749 in German, although there have been changes to the interpretation of the word over time.

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History of the function concept

The mathematical concept of a function emerged in the 17th century in connection with the development of the calculus; for example, the slope \operatorname\!y/\operatorname\!x of a graph at a point was regarded as a function of the x-coordinate of the point.

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History of trigonometry

Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics.

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Horner's method

In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S..) is either of two things.

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Hypatia

Hypatia (born 350–370; died 415 AD) was a Hellenistic Neoplatonist philosopher, astronomer, and mathematician, who lived in Alexandria, Egypt, then part of the Eastern Roman Empire.

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Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

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Hypercomplex number

In mathematics, a hypercomplex number is a traditional term for an element of a unital algebra over the field of real numbers.

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Hyperreal number

The system of hyperreal numbers is a way of treating infinite and infinitesimal quantities.

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Iberian Peninsula

The Iberian Peninsula, also known as Iberia, is located in the southwest corner of Europe.

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Ibn al-Haytham

Hasan Ibn al-Haytham (Latinized Alhazen; full name أبو علي، الحسن بن الحسن بن الهيثم) was an Arab mathematician, astronomer, and physicist of the Islamic Golden Age.

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Imaginary number

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit,j is usually used in Engineering contexts where i has other meanings (such as electrical current) which is defined by its property.

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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

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Independence (mathematical logic)

In mathematical logic, independence refers to the unprovability of a sentence from other sentences.

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Indeterminate equation

An indeterminate equation, in mathematics, is an equation for which there is more than one solution; for example, 2x.

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Indian mathematics

Indian mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century.

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Indus River

The Indus River (also called the Sindhū) is one of the longest rivers in Asia.

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Indus Valley Civilisation

The Indus Valley Civilisation (IVC), or Harappan Civilisation, was a Bronze Age civilisation (5500–1300 BCE; mature period 2600–1900 BCE) mainly in the northwestern regions of South Asia, extending from what today is northeast Afghanistan to Pakistan and northwest India.

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Industry

Industry is the production of goods or related services within an economy.

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Infinitesimal

In mathematics, infinitesimals are things so small that there is no way to measure them.

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Information theory

Information theory studies the quantification, storage, and communication of information.

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Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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International Congress of Mathematicians

The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics.

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Iran

Iran (ایران), also known as Persia, officially the Islamic Republic of Iran (جمهوری اسلامی ایران), is a sovereign state in Western Asia. With over 81 million inhabitants, Iran is the world's 18th-most-populous country. Comprising a land area of, it is the second-largest country in the Middle East and the 17th-largest in the world. Iran is bordered to the northwest by Armenia and the Republic of Azerbaijan, to the north by the Caspian Sea, to the northeast by Turkmenistan, to the east by Afghanistan and Pakistan, to the south by the Persian Gulf and the Gulf of Oman, and to the west by Turkey and Iraq. The country's central location in Eurasia and Western Asia, and its proximity to the Strait of Hormuz, give it geostrategic importance. Tehran is the country's capital and largest city, as well as its leading economic and cultural center. Iran is home to one of the world's oldest civilizations, beginning with the formation of the Elamite kingdoms in the fourth millennium BCE. It was first unified by the Iranian Medes in the seventh century BCE, reaching its greatest territorial size in the sixth century BCE, when Cyrus the Great founded the Achaemenid Empire, which stretched from Eastern Europe to the Indus Valley, becoming one of the largest empires in history. The Iranian realm fell to Alexander the Great in the fourth century BCE and was divided into several Hellenistic states. An Iranian rebellion culminated in the establishment of the Parthian Empire, which was succeeded in the third century CE by the Sasanian Empire, a leading world power for the next four centuries. Arab Muslims conquered the empire in the seventh century CE, displacing the indigenous faiths of Zoroastrianism and Manichaeism with Islam. Iran made major contributions to the Islamic Golden Age that followed, producing many influential figures in art and science. After two centuries, a period of various native Muslim dynasties began, which were later conquered by the Turks and the Mongols. The rise of the Safavids in the 15th century led to the reestablishment of a unified Iranian state and national identity, with the country's conversion to Shia Islam marking a turning point in Iranian and Muslim history. Under Nader Shah, Iran was one of the most powerful states in the 18th century, though by the 19th century, a series of conflicts with the Russian Empire led to significant territorial losses. Popular unrest led to the establishment of a constitutional monarchy and the country's first legislature. A 1953 coup instigated by the United Kingdom and the United States resulted in greater autocracy and growing anti-Western resentment. Subsequent unrest against foreign influence and political repression led to the 1979 Revolution and the establishment of an Islamic republic, a political system that includes elements of a parliamentary democracy vetted and supervised by a theocracy governed by an autocratic "Supreme Leader". During the 1980s, the country was engaged in a war with Iraq, which lasted for almost nine years and resulted in a high number of casualties and economic losses for both sides. According to international reports, Iran's human rights record is exceptionally poor. The regime in Iran is undemocratic, and has frequently persecuted and arrested critics of the government and its Supreme Leader. Women's rights in Iran are described as seriously inadequate, and children's rights have been severely violated, with more child offenders being executed in Iran than in any other country in the world. Since the 2000s, Iran's controversial nuclear program has raised concerns, which is part of the basis of the international sanctions against the country. The Joint Comprehensive Plan of Action, an agreement reached between Iran and the P5+1, was created on 14 July 2015, aimed to loosen the nuclear sanctions in exchange for Iran's restriction in producing enriched uranium. Iran is a founding member of the UN, ECO, NAM, OIC, and OPEC. It is a major regional and middle power, and its large reserves of fossil fuels – which include the world's largest natural gas supply and the fourth-largest proven oil reserves – exert considerable influence in international energy security and the world economy. The country's rich cultural legacy is reflected in part by its 22 UNESCO World Heritage Sites, the third-largest number in Asia and eleventh-largest in the world. Iran is a multicultural country comprising numerous ethnic and linguistic groups, the largest being Persians (61%), Azeris (16%), Kurds (10%), and Lurs (6%).

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Iraq

Iraq (or; العراق; عێراق), officially known as the Republic of Iraq (جُمُهورية العِراق; کۆماری عێراق), is a country in Western Asia, bordered by Turkey to the north, Iran to the east, Kuwait to the southeast, Saudi Arabia to the south, Jordan to the southwest and Syria to the west.

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Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

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Ishango bone

The Ishango bone is a bone tool, dated to the Upper Paleolithic era.

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Isidore of Miletus

Isidore of Miletus (Ἰσίδωρος ὁ Μιλήσιος; Medieval Greek pronunciation:; Isidorus Miletus) was one of the two main Byzantine Greek architects (Anthemius of Tralles was the other) that Emperor Justinian I commissioned to design the cathedral Hagia Sophia in Constantinople from 532 to 537.

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Italy

Italy (Italia), officially the Italian Republic (Repubblica Italiana), is a sovereign state in Europe.

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Jacopo de' Barbari

Jacopo de' Barbari, sometimes known or referred to as de'Barbari, de Barberi, de Barbari, Barbaro, Barberino, Barbarigo or Barberigo (c. 1460/70 – before 1516), was an Italian painter and printmaker with a highly individual style.

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Jade Mirror of the Four Unknowns

Jade Mirror of the Four Unknowns, Siyuan yujian (四元玉鉴), also referred to as Jade Mirror of the Four Origins, is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie.

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Jamshīd al-Kāshī

Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī) (غیاث الدین جمشید کاشانی Ghiyās-ud-dīn Jamshīd Kāshānī) (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer and mathematician.

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Japanese mathematics

denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867).

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János Bolyai

János Bolyai (15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines.

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Jean Dieudonné

Jean Alexandre Eugène Dieudonné (1 July 1906 – 29 November 1992) was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology.

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Jean-Pierre Serre

Jean-Pierre Serre (born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory.

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Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.

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John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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John Napier

John Napier of Merchiston (1550 – 4 April 1617); also signed as Neper, Nepair; nicknamed Marvellous Merchiston) was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioannes Neper. John Napier is best known as the discoverer of logarithms. He also invented the so-called "Napier's bones" and made common the use of the decimal point in arithmetic and mathematics. Napier's birthplace, Merchiston Tower in Edinburgh, is now part of the facilities of Edinburgh Napier University. Napier died from the effects of gout at home at Merchiston Castle and his remains were buried in the kirkyard of St Giles. Following the loss of the kirkyard there to build Parliament House, he was memorialised at St Cuthbert's at the west side of Edinburgh.

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John von Neumann

John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Jost Bürgi

Jost Bürgi (also Joost, Jobst; Latinized surname Burgius or Byrgius; 28 February 1552 – 31 January 1632), active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician.

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Julian calendar

The Julian calendar, proposed by Julius Caesar in 46 BC (708 AUC), was a reform of the Roman calendar.

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Julius Caesar

Gaius Julius Caesar (12 or 13 July 100 BC – 15 March 44 BC), known by his cognomen Julius Caesar, was a Roman politician and military general who played a critical role in the events that led to the demise of the Roman Republic and the rise of the Roman Empire.

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Justinian I

Justinian I (Flavius Petrus Sabbatius Iustinianus Augustus; Flávios Pétros Sabbátios Ioustinianós; 482 14 November 565), traditionally known as Justinian the Great and also Saint Justinian the Great in the Eastern Orthodox Church, was the Eastern Roman emperor from 527 to 565.

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Jyeṣṭhadeva

Jyeṣṭhadeva (Malayalam: ജ്യേഷ്ഠദേവന്) was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Sangamagrama Madhava.

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Kalman filter

Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe.

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Karl Weierstrass

Karl Theodor Wilhelm Weierstrass (Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".

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Kenneth Appel

Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an American mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana-Champaign, solved one of the most famous problems in mathematics, the four-color theorem.

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Kenneth O. May Prize

Kenneth O. May Prize and Medal in history of mathematics is an award of the International Commission on the History of Mathematics (ICHM) "for the encouragement and promotion of the history of mathematics internationally".

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Kepler conjecture

The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space.

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Kepler's laws of planetary motion

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

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Kerala School of Astronomy and Mathematics

The Kerala School of Astronomy and Mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar.

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Klein's encyclopedia

Klein's encyclopedia is a German mathematical encyclopedia published in six volumes from 1898 to 1933.

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Knot theory

In topology, knot theory is the study of mathematical knots.

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Korean numerals

The Korean language has two regularly used sets of numerals, a native Korean system and Sino-Korean system.

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Kurt Gödel

Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.

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L. E. J. Brouwer

Luitzen Egbertus Jan Brouwer (27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis.

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Latin translations of the 12th century

Latin translations of the 12th century were spurred by a major search by European scholars for new learning unavailable in western Europe at the time; their search led them to areas of southern Europe, particularly in central Spain and Sicily, which recently had come under Christian rule following their reconquest in the late 11th century.

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Latins (Italic tribe)

The Latins (Latin: Latini), sometimes known as the Latians, were an Italic tribe which included the early inhabitants of the city of Rome.

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Laurent Schwartz

Laurent-Moïse Schwartz (5 March 1915 – 4 July 2002) was a French mathematician.

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Leap year

A leap year (also known as an intercalary year or bissextile year) is a calendar year containing one additional day (or, in the case of lunisolar calendars, a month) added to keep the calendar year synchronized with the astronomical or seasonal year.

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Lebesgue integration

In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis.

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Leibniz formula for π

In mathematics, the Leibniz formula for pi, named after Gottfried Leibniz, states that It is also called Madhava–Leibniz series as it is a special case of a more general series expansion for the inverse tangent function, first discovered by the Indian mathematician Madhava of Sangamagrama in the 14th century, the specific case first published by Leibniz around 1676.

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Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

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Liber Abaci

Liber Abaci (1202, also spelled as Liber Abbaci) is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci.

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Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

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Lie group

In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.

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Lie theory

In mathematics, the researcher Sophus Lie initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory.

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Limit of a function

Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.

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Linear equation

In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.

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List of important publications in mathematics

This is a list of important publications in mathematics, organized by field.

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List of mathematics history topics

This is a list of mathematics history topics, by Wikipedia page.

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List of Roman taxes

This is a list of the taxes levied by Rome.

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Lists of mathematicians

This is a list of lists of mathematicians. Lists by nationality, ethnicity or religion.

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Liu Hui

Liu Hui was a Chinese mathematician who lived in the state of Cao Wei during the Three Kingdoms period (220–280) of China.

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Liu Hui's π algorithm

Liu Hui's algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the Cao Wei Kingdom.

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Liu Xin

Liu Xin (c. 50 BCE – 23 CE), courtesy name Zijun, was a Chinese astronomer, historian, librarian and politician during the Western Han Dynasty (206 BCE – 9 CE) and Xin Dynasty (9 – 23 CE).

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Lodovico Ferrari

Lodovico de Ferrari (2 February 1522 – 5 October 1565) was an Italian mathematician.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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London Mathematical Society

The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).

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Luca Pacioli

Fra Luca Bartolomeo de Pacioli (sometimes Paccioli or Paciolo; 1447–1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and a seminal contributor to the field now known as accounting.

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Lucas–Lehmer primality test

In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers.

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Lunar calendar

A lunar calendar is a calendar based upon the monthly cycles of the Moon's phases (synodic months), in contrast to solar calendars, whose annual cycles are based only directly upon the solar year.

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Madhava of Sangamagrama

Mādhava of Sangamagrāma, was a mathematician and astronomer from the town of Sangamagrama (believed to be present-day Aloor, Irinjalakuda in Thrissur District), Kerala, India.

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Magic circle (mathematics)

Magic circles were invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui (c. 1238–1298).

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Magic square

In recreational mathematics and combinatorial design, a magic square is a n\times n square grid (where is the number of cells on each side) filled with distinct positive integers in the range 1,2,...,n^2 such that each cell contains a different integer and the sum of the integers in each row, column and diagonal is equal.

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Magnitude (mathematics)

In mathematics, magnitude is the size of a mathematical object, a property which determines whether the object is larger or smaller than other objects of the same kind.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Mathematical Association of America

The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.

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Mathematical induction

Mathematical induction is a mathematical proof technique.

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Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

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Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas.

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Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.

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Mathematical proof

In mathematics, a proof is an inferential argument for a mathematical statement.

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Mathematical puzzle

Mathematical puzzles make up an integral part of recreational mathematics.

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Mathematical structure

In mathematics, a structure on a set is an additional mathematical object that, in some manner, attaches (or relates) to that set to endow it with some additional meaning or significance.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Mathematics in medieval Islam

Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).

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Mathematics Subject Classification

The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme collaboratively produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Matteo Ricci

Matteo Ricci, S.J. (Mattheus Riccius Maceratensis; 6 October 1552 – 11 May 1610), was an Italian Jesuit priest and one of the founding figures of the Jesuit China missions.

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Maya astronomy

Maya astronomy is the study of the Moon, planets, Milky Way, Sun, and other astronomical occurrences by the Precolumbian Maya Civilization of Mesoamerica.

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Maya calendar

The Maya calendar is a system of calendars used in pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico.

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Maya civilization

The Maya civilization was a Mesoamerican civilization developed by the Maya peoples, and noted for its hieroglyphic script—the only known fully developed writing system of the pre-Columbian Americas—as well as for its art, architecture, mathematics, calendar, and astronomical system.

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Maya numerals

The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization.

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Mean value theorem

In mathematics, the mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

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Measure (mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

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Mechanical engineering

Mechanical engineering is the discipline that applies engineering, physics, engineering mathematics, and materials science principles to design, analyze, manufacture, and maintain mechanical systems.

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Megalith

A megalith is a large stone that has been used to construct a structure or monument, either alone or together with other stones.

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Menelaus of Alexandria

Menelaus of Alexandria (Μενέλαος ὁ Ἀλεξανδρεύς, Menelaos ho Alexandreus; c. 70 – 140 CE) was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines.

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Menelaus's theorem

Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry.

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Mental calculator

Mental calculators are people with a prodigious ability in some area of mental calculation, such as adding, subtracting, multiplying or dividing large numbers.

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Mesopotamia

Mesopotamia is a historical region in West Asia situated within the Tigris–Euphrates river system, in modern days roughly corresponding to most of Iraq, Kuwait, parts of Northern Saudi Arabia, the eastern parts of Syria, Southeastern Turkey, and regions along the Turkish–Syrian and Iran–Iraq borders.

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Method of exhaustion

The method of exhaustion (methodus exhaustionibus, or méthode des anciens) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.

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Metre (music)

In music, metre (Am. meter) refers to the regularly recurring patterns and accents such as bars and beats.

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Metre (poetry)

In poetry, metre is the basic rhythmic structure of a verse or lines in verse.

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Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

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Metrology

Metrology is the science of measurement.

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Mexico

Mexico (México; Mēxihco), officially called the United Mexican States (Estados Unidos Mexicanos) is a federal republic in the southern portion of North America.

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Middle Ages

In the history of Europe, the Middle Ages (or Medieval Period) lasted from the 5th to the 15th century.

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Middle East

The Middle Easttranslit-std; translit; Orta Şərq; Central Kurdish: ڕۆژھەڵاتی ناوین, Rojhelatî Nawîn; Moyen-Orient; translit; translit; translit; Rojhilata Navîn; translit; Bariga Dhexe; Orta Doğu; translit is a transcontinental region centered on Western Asia, Turkey (both Asian and European), and Egypt (which is mostly in North Africa).

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Middle Kingdom of Egypt

The Middle Kingdom of Egypt (also known as The Period of Reunification) is the period in the history of ancient Egypt between circa 2050 BC and 1710 BC, stretching from the reunification of Egypt under the impulse of Mentuhotep II of the Eleventh Dynasty to the end of the Twelfth Dynasty.

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Milü

The name Milü ("close ratio"), also known as Zulü (Zu's ratio), is given to an approximation to pi (pi) found by Chinese mathematician and astronomer, Zǔ Chōngzhī (祖沖之).

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Mile

The mile is an English unit of length of linear measure equal to 5,280 feet, or 1,760 yards, and standardised as exactly 1,609.344 metres by international agreement in 1959.

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Millennium Prize Problems

The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.

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Ming dynasty

The Ming dynasty was the ruling dynasty of China – then known as the – for 276 years (1368–1644) following the collapse of the Mongol-led Yuan dynasty.

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Model theory

In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.

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Modern history

Modern history, the modern period or the modern era, is the linear, global, historiographical approach to the time frame after post-classical history.

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Modular form

In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.

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Mohism

Mohism or Moism was an ancient Chinese philosophy of logic, rational thought and science developed by the academic scholars who studied under the ancient Chinese philosopher Mozi (c. 470 BC – c. 391 BC) and embodied in an eponymous book: the Mozi.

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Morris Kline

Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.

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Mosaics of Delos

The mosaics of Delos are a significant body of ancient Greek mosaic art.

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Moscow Mathematical Papyrus

The Moscow Mathematical Papyrus is an ancient Egyptian mathematical papyrus, also called the Golenishchev Mathematical Papyrus, after its first owner outside of Egypt, Egyptologist Vladimir Golenishchev.

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Mozi

Mozi (Latinized as Micius; c. 470 – c. 391 BC), original name Mo Di (墨翟), was a Chinese philosopher during the Hundred Schools of Thought period (early Warring States period).

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Muhammad ibn Musa al-Khwarizmi

There is some confusion in the literature on whether al-Khwārizmī's full name is ابو عبد الله محمد بن موسى الخوارزمي or ابو جعفر محمد بن موسی الخوارزمی.

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Multiplication table

In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.

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Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.

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Musaeum

The Musaeum or Mouseion at Alexandria (Μουσεῖον τῆς Ἀλεξανδρείας), which included the famous Library of Alexandria, was an institution founded by Ptolemy I Soter or, perhaps more likely, by his son Ptolemy II Philadelphus.

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Museo di Capodimonte

Museo di Capodimonte is an art museum located in the Palace of Capodimonte, a grand Bourbon palazzo in Naples, Italy.

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Napoleon

Napoléon Bonaparte (15 August 1769 – 5 May 1821) was a French statesman and military leader who rose to prominence during the French Revolution and led several successful campaigns during the French Revolutionary Wars.

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Nasir al-Din al-Tusi

Muhammad ibn Muhammad ibn al-Hasan al-Tūsī (محمد بن محمد بن حسن طوسی‎ 18 February 1201 – 26 June 1274), better known as Nasir al-Din Tusi (نصیر الدین طوسی; or simply Tusi in the West), was a Persian polymath, architect, philosopher, physician, scientist, and theologian.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Nature (journal)

Nature is a British multidisciplinary scientific journal, first published on 4 November 1869.

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Negative number

In mathematics, a negative number is a real number that is less than zero.

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Neopythagoreanism

Neopythagoreanism (or Neo-Pythagoreanism) was a school of Hellenistic philosophy which revived Pythagorean doctrines.

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Niccolò Fontana Tartaglia

Niccolò Fontana Tartaglia (1499/1500, Brescia – 13 December 1557, Venice) was a Venetian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then-Republic of Venice (now part of Italy).

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Nicolas Bourbaki

Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935.

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Nicole Oresme

Nicole Oresme (c. 1320–1325 – July 11, 1382), also known as Nicolas Oresme, Nicholas Oresme, or Nicolas d'Oresme, was a significant philosopher of the later Middle Ages.

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Nicomachus

Nicomachus of Gerasa (Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek.

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Niels Henrik Abel

Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields.

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Nikolai Lobachevsky

Nikolai Ivanovich Lobachevsky (a; –) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry and also his fundamental study on Dirichlet integrals known as Lobachevsky integral formula.

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Nile

The Nile River (النيل, Egyptian Arabic en-Nīl, Standard Arabic an-Nīl; ⲫⲓⲁⲣⲱ, P(h)iaro; Ancient Egyptian: Ḥ'pī and Jtrw; Biblical Hebrew:, Ha-Ye'or or, Ha-Shiḥor) is a major north-flowing river in northeastern Africa, and is commonly regarded as the longest river in the world, though some sources cite the Amazon River as the longest.

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Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.

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Non-standard analysis

The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.

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Noncommutative ring

In mathematics, more specifically abstract algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exists a and b in R with a·b ≠ b·a.

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North Africa

North Africa is a collective term for a group of Mediterranean countries and territories situated in the northern-most region of the African continent.

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Number

A number is a mathematical object used to count, measure and also label.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Numeral system

A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

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Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

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Numerical digit

A numerical digit is a single symbol (such as "2" or "5") used alone, or in combinations (such as "25"), to represent numbers (such as the number 25) according to some positional numeral systems.

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Odometer

An odometer or odograph is an instrument used for measuring the distance travelled by a vehicle, such as a bicycle or car.

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Omar Khayyam

Omar Khayyam (عمر خیّام; 18 May 1048 – 4 December 1131) was a Persian mathematician, astronomer, and poet.

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Open access

Open access (OA) refers to research outputs which are distributed online and free of cost or other barriers, and possibly with the addition of a Creative Commons license to promote reuse.

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Operations research

Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.

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Optics

Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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Opus tessellatum

Opus tessellatum is the Latin name for the normal technique of Greek and Roman mosaic, made from tesserae that are larger than about 4 mm.

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Opus vermiculatum

Opus vermiculatum is a method of laying mosaic tesserae to emphasise an outline around a subject.

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Ottoman Empire

The Ottoman Empire (دولت عليه عثمانیه,, literally The Exalted Ottoman State; Modern Turkish: Osmanlı İmparatorluğu or Osmanlı Devleti), also historically known in Western Europe as the Turkish Empire"The Ottoman Empire-also known in Europe as the Turkish Empire" or simply Turkey, was a state that controlled much of Southeast Europe, Western Asia and North Africa between the 14th and early 20th centuries.

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Oxford Calculators

The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford; for this reason they were dubbed "The Merton School".

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P-adic number

In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

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Paolo Ruffini

Paolo Ruffini (September 22, 1765 – May 10, 1822) was an Italian mathematician and philosopher.

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Pappus configuration

In geometry, the Pappus configuration is a configuration of nine points and nine lines in the Euclidean plane, with three points per line and three lines through each point.

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Pappus graph

In the mathematical field of graph theory, the Pappus graph is a bipartite 3-regular undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration.

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Pappus of Alexandria

Pappus of Alexandria (Πάππος ὁ Ἀλεξανδρεύς; c. 290 – c. 350 AD) was one of the last great Greek mathematicians of Antiquity, known for his Synagoge (Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry.

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Pappus's centroid theorem

In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution.

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Pappus's hexagon theorem

In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear, lying on the Pappus line.

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Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

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Paraboloid

In geometry, a paraboloid is a quadric surface that has (exactly) one axis of symmetry and no center of symmetry.

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Parallel postulate

In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.

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Parameter space

In science, a parameter space is the set of all possible combinations of values for all the different parameters contained in a particular mathematical model.

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Paris

Paris is the capital and most populous city of France, with an area of and a population of 2,206,488.

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Partition (number theory)

In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.

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Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

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Pascal's Wager

Pascal's Wager is an argument in philosophy presented by the seventeenth-century French philosopher, mathematician and physicist Blaise Pascal (1623–62).

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Paul Cohen

Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician.

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Paul Erdős

Paul Erdős (Erdős Pál; 26 March 1913 – 20 September 1996) was a Hungarian mathematician.

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Paul Hoffman (science writer)

Paul Hoffman (born March 30, 1956) is the president and CEO of the Liberty Science Center in Jersey City, New Jersey.

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Pāṇini

(पाणिनि, Frits Staal (1965),, Philosophy East and West, Vol. 15, No. 2 (Apr., 1965), pp. 99-116) is an ancient Sanskrit philologist, grammarian, and a revered scholar in Hinduism.

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Peano axioms

In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.

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Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

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Persian people

The Persians--> are an Iranian ethnic group that make up over half the population of Iran.

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Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

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Pi

The number is a mathematical constant.

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Piero della Francesca

Piero della Francesca (c. 1415 – 12 October 1492) was an Italian painter of the Early Renaissance.

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Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

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Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.

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Pingala

Pingala (Devanagari: पिङ्गल) (c. 3rd/2nd century BC) was an ancient Indian mathematician who authored the (also called Pingala-sutras), the earliest known treatise on Sanskrit prosody.

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Plato

Plato (Πλάτων Plátōn, in Classical Attic; 428/427 or 424/423 – 348/347 BC) was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world.

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Platonic Academy

The Academy (Ancient Greek: Ἀκαδημία) was founded by Plato (428/427 BC – 348/347 BC) in ca.

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Plimpton 322

Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics.

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Plus and minus signs

The plus and minus signs (+ and −) are mathematical symbols used to represent the notions of positive and negative as well as the operations of addition and subtraction.

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Poincaré conjecture

In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.

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Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Pope Gregory XIII

Pope Gregory XIII (Gregorius XIII; 7 January 1502 – 10 April 1585), born Ugo Boncompagni, was Pope of the Catholic Church from 13 May 1572 to his death in 1585.

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Positional notation

Positional notation or place-value notation is a method of representing or encoding numbers.

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Post-classical history

Post-classical history (also called the Post-Antiquity era, Post-Ancient Era, or Pre-Modern Era) is a periodization commonly used by the school of "world history" instead of Middle Ages (Medieval) which is roughly synonymous.

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Pre-Columbian era

The Pre-Columbian era incorporates all period subdivisions in the history and prehistory of the Americas before the appearance of significant European influences on the American continents, spanning the time of the original settlement in the Upper Paleolithic period to European colonization during the Early Modern period.

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Prehistoric Egypt

The prehistory of Egypt spans the period from earliest human settlement to the beginning of the Early Dynastic Period of Egypt around 3100 BC, starting with the first Pharaoh, Narmer for some egyptologists, Hor-Aha for others, (also known as Menes).

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Prehistory

Human prehistory is the period between the use of the first stone tools 3.3 million years ago by hominins and the invention of writing systems.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Private school

Private schools, also known to many as independent schools, non-governmental, privately funded, or non-state schools, are not administered by local, state or national governments.

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Probability theory

Probability theory is the branch of mathematics concerned with probability.

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Proclus

Proclus Lycaeus (8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius).

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Proportionality (mathematics)

In mathematics, two variables are proportional if there is always a constant ratio between them.

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Pseudonym

A pseudonym or alias is a name that a person or group assumes for a particular purpose, which can differ from their first or true name (orthonym).

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Ptolemy

Claudius Ptolemy (Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos; Claudius Ptolemaeus) was a Greco-Roman mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology.

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Ptolemy's theorem

In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle).

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Public-key cryptography

Public-key cryptography, or asymmetric cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner.

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Pure mathematics

Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.

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Pyramid

A pyramid (from πυραμίς) is a structure whose outer surfaces are triangular and converge to a single point at the top, making the shape roughly a pyramid in the geometric sense.

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Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement.

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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

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Pythagorean triple

A Pythagorean triple consists of three positive integers,, and, such that.

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Pythagoreanism

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism.

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Qin dynasty

The Qin dynasty was the first dynasty of Imperial China, lasting from 221 to 206 BC.

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Qin Shi Huang

Qin Shi Huang (18 February 25910 September 210) was the founder of the Qin dynasty and was the first emperor of a unified China.

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Quadratic equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.

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Quadratic reciprocity

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.

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Quadrivium

The quadrivium (plural: quadrivia) is the four subjects, or arts, taught after teaching the trivium.

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Quantification (science)

In mathematics and empirical science, quantification (or quantitation) is the act of counting and measuring that maps human sense observations and experiences into quantities.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Quartic function

In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.

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Quaternion Society

A scientific society, the Quaternion Society was an "International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics".

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Radius

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

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Radix

In mathematical numeral systems, the radix or base is the number of unique digits, including zero, used to represent numbers in a positional numeral system.

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Rafael Bombelli

Rafael Bombelli (baptised on 20 January 1526; died 1572) was an Italian mathematician.

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Ramanujan theta function

In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties.

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Ratio

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.

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Rózsa Péter

Rózsa Péter, born Politzer, (17 February 1905 – 16 February 1977) was a Hungarian mathematician and logician.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Recursion

Recursion occurs when a thing is defined in terms of itself or of its type.

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Reduction (mathematics)

In mathematics, reduction refers to the rewriting of an expression into a simpler form.

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Regular number

Regular numbers are numbers that evenly divide powers of 60 (or, equivalently powers of 30).

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Religion in ancient Rome

Religion in Ancient Rome includes the ancestral ethnic religion of the city of Rome that the Romans used to define themselves as a people, as well as the religious practices of peoples brought under Roman rule, in so far as they became widely followed in Rome and Italy.

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Renaissance

The Renaissance is a period in European history, covering the span between the 14th and 17th centuries.

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René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

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René Thom

René Frédéric Thom (2 September 1923 – 25 October 2002) was a French mathematician.

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Rhetorical modes

Rhetorical modes (also known as modes of discourse) describe the variety, conventions, and purposes of the major kinds of language-based communication, particularly writing and speaking.

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Rhind Mathematical Papyrus

The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of Egyptian mathematics.

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Riemannian geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.

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Right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).

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Rigour

Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness.

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Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

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Robert of Chester

Robert of Chester (Latin: Robertus Castrensis) was an English Arabist of the 12th century.

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Roman art

Roman art refers to the visual arts made in Ancient Rome and in the territories of the Roman Empire.

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Roman bridge

Roman bridges, built by ancient Romans, were the first large and lasting bridges built.

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Roman calendar

The Roman calendar was the calendar used by the Roman kingdom and republic.

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Roman Empire

The Roman Empire (Imperium Rōmānum,; Koine and Medieval Greek: Βασιλεία τῶν Ῥωμαίων, tr.) was the post-Roman Republic period of the ancient Roman civilization, characterized by government headed by emperors and large territorial holdings around the Mediterranean Sea in Europe, Africa and Asia.

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Roman engineering

Romans are famous for their advanced engineering accomplishments, although some of their own inventions were improvements on older ideas, concepts and inventions.

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Roman Kingdom

The Roman Kingdom, or regal period, was the period of the ancient Roman civilization characterized by a monarchical form of government of the city of Rome and its territories.

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Roman military engineering

The military engineering of Ancient Rome's armed forces was of a scale and frequency far beyond that of any of its contemporaries'.

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Roman mosaic

A Roman mosaic is a mosaic made during the Roman period, throughout the Roman Republic and later Empire.

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Roman numerals

The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages.

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Roman Republic

The Roman Republic (Res publica Romana) was the era of classical Roman civilization beginning with the overthrow of the Roman Kingdom, traditionally dated to 509 BC, and ending in 27 BC with the establishment of the Roman Empire.

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Roman roads

Roman roads (Latin: viae Romanae; singular: via Romana meaning "Roman way") were physical infrastructure vital to the maintenance and development of the Roman state, and were built from about 300 BC through the expansion and consolidation of the Roman Republic and the Roman Empire.

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Roman technology

Roman technology is the engineering practice which supported Roman civilization and made the expansion of Roman commerce and Roman military possible for over a millennium (753 BC–476 AD).

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RSA (cryptosystem)

RSA (Rivest–Shamir–Adleman) is one of the first public-key cryptosystems and is widely used for secure data transmission.

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Safavid dynasty

The Safavid dynasty (دودمان صفوی Dudmān e Safavi) was one of the most significant ruling dynasties of Iran, often considered the beginning of modern Iranian history.

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Sanskrit grammar

The grammar of the Sanskrit language has a complex verbal system, rich nominal declension, and extensive use of compound nouns.

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Science and technology of the Han dynasty

The Han dynasty (206 BCE – 220 CE) of ancient China, divided between the eras of Western Han (206 BCE – 9 CE, when the capital was at Chang'an), Xin dynasty of Wang Mang (r. AD 9–23), and Eastern Han (25–220 CE, when the capital was at Luoyang, and after 196 CE at Xuchang), witnessed some of the most significant advancements in premodern Chinese science and technology.

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Scientific journal

In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research.

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Scipione del Ferro

Scipione del Ferro (6 February 1465 – 5 November 1526) was an Italian mathematician who first discovered a method to solve the depressed cubic equation.

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Scotland

Scotland (Alba) is a country that is part of the United Kingdom and covers the northern third of the island of Great Britain.

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Seleucid Empire

The Seleucid Empire (Βασιλεία τῶν Σελευκιδῶν, Basileía tōn Seleukidōn) was a Hellenistic state ruled by the Seleucid dynasty, which existed from 312 BC to 63 BC; Seleucus I Nicator founded it following the division of the Macedonian empire vastly expanded by Alexander the Great.

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Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

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Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Seven Bridges of Königsberg

The Seven Bridges of Königsberg is a historically notable problem in mathematics.

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Sexagesimal

Sexagesimal (base 60) is a numeral system with sixty as its base.

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Sheaf (mathematics)

In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.

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Shulba Sutras

The Shulba Sutras or Śulbasūtras (Sanskrit: "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction.

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Siculus Flaccus

Siculus Flaccus (date uncertain) was an ancient Roman gromaticus (land surveyor), and writer in Latin on land surveying.

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Sieve of Eratosthenes

In mathematics, the sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit.

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Signal processing

Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.

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Simon Stevin

Simon Stevin (1548–1620), sometimes called Stevinus, was a Flemish mathematician, physicist and military engineer.

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Simplex algorithm

In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.

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Simplicius of Cilicia

Simplicius of Cilicia (Σιμπλίκιος ὁ Κίλιξ; c. 490 – c. 560) was a disciple of Ammonius Hermiae and Damascius, and was one of the last of the Neoplatonists.

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Singularity theory

In mathematics, singularity theory studies spaces that are almost manifolds, but not quite.

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Six Degrees of Kevin Bacon

Six Degrees of Kevin Bacon is a parlor game based on the "six degrees of separation" concept, which posits that any two people on Earth are six or fewer acquaintance links apart.

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Société mathématique de France

The Société Mathématique de France (SMF) is the main professional society of French mathematicians.

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Society of Jesus

The Society of Jesus (SJ – from Societas Iesu) is a scholarly religious congregation of the Catholic Church which originated in sixteenth-century Spain.

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Solar calendar

A solar calendar is a calendar whose dates indicate the season or almost equivalently the position of the apparent position of the sun in relative to the stars.

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Solid geometry

In mathematics, solid geometry is the traditional name for the geometry of three-dimensional Euclidean space.

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Song dynasty

The Song dynasty (960–1279) was an era of Chinese history that began in 960 and continued until 1279.

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Sosigenes of Alexandria

Sosigenes of Alexandria (Σωσιγένης ὁ Ἀλεξανδρεύς) was a Greek astronomer from Ptolemaic Egypt who, according to Roman historian Pliny the Elder, was consulted by Julius Caesar for the design of the Julian calendar.

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Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

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Spherical geometry

Spherical geometry is the geometry of the two-dimensional surface of a sphere.

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Spherical trigonometry

Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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Squaring the circle

Squaring the circle is a problem proposed by ancient geometers.

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Srinivasa Ramanujan

Srinivasa Ramanujan (22 December 188726 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable.

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St. Lawrence University

St.

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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Structural engineering

Structural engineering is that part of civil engineering in which structural engineers are educated to create the 'bones and muscles' that create the form and shape of man made structures.

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Suanpan

The suanpan, also spelled suan pan or souanpan) is an abacus of Chinese origin first described in a 190 CE book of the Eastern Han Dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue. However, the exact design of this suanpan is not known. Usually, a suanpan is about 20 cm (8 in) tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads on each rod in the bottom deck. This configuration is used for both decimal and hexadecimal computation. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. The suanpan can be reset to the starting position instantly by a quick jerk around the horizontal axis to spin all the beads away from the horizontal beam at the center. Suanpans can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed. The modern suanpan has 4+1 beads, colored beads to indicate position and a clear-all button. When the clear-all button is pressed, two mechanical levers push the top row beads to the top position and the bottom row beads to the bottom position, thus clearing all numbers to zero. This replaces clearing the beads by hand, or quickly rotating the suanpan around its horizontal center line to clear the beads by centrifugal force.

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Sumer

SumerThe name is from Akkadian Šumeru; Sumerian en-ĝir15, approximately "land of the civilized kings" or "native land".

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Summa de arithmetica

Summa de arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) is a book on mathematics written by Luca Pacioli and first published in 1494.

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Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

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Surface area

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

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Surface of revolution

A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) around an axis of rotation.

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Surreal number

In mathematics, the surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number.

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Surveying

Surveying or land surveying is the technique, profession, and science of determining the terrestrial or three-dimensional positions of points and the distances and angles between them.

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Symmetry

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.

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Syracuse, Sicily

Syracuse (Siracusa,; Sarausa/Seragusa; Syrācūsae; Συράκουσαι, Syrakousai; Medieval Συρακοῦσαι) is a historic city on the island of Sicily, the capital of the Italian province of Syracuse.

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Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

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Tessera

A tessera (plural: tesserae, diminutive tessella) is an individual tile, usually formed in the shape of a cube, used in creating a mosaic.

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Tetrabiblos

Tetrabiblos (Τετράβιβλος) 'four books', also known in Greek as Apotelesmatiká (Ἀποτελεσματικά) "Effects", and in Latin as Quadripartitum "Four Parts", is a text on the philosophy and practice of astrology, written in the 2nd century AD by the Alexandrian scholar Claudius Ptolemy (AD 90– AD 168).

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Thales of Miletus

Thales of Miletus (Θαλῆς (ὁ Μιλήσιος), Thalēs; 624 – c. 546 BC) was a pre-Socratic Greek philosopher, mathematician, and astronomer from Miletus in Asia Minor (present-day Milet in Turkey).

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Thales's theorem

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line is a diameter, then the angle ∠ABC is a right angle.

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The Compendious Book on Calculation by Completion and Balancing

The Compendious Book on Calculation by Completion and Balancing (الكتاب المختصر في حساب الجبر والمقابلة, Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala; Liber Algebræ et Almucabola) is an Arabic treatise on mathematics written by Persian polymath Muḥammad ibn Mūsā al-Khwārizmī around 820 CE while he was in the Abbasid capital of Baghdad.

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The Nine Chapters on the Mathematical Art

The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE.

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The Story of Maths

The Story of Maths is a four-part British television series outlining aspects of the history of mathematics.

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Theory

A theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking.

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Thomas Bradwardine

Thomas Bradwardine (c. 1300 – 26 August 1349) was an English cleric, scholar, mathematician, physicist, courtier and, very briefly, Archbishop of Canterbury.

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Thomas Callister Hales

Thomas Callister Hales (born June 4, 1958) is an American mathematician working in the areas of representation theory, discrete geometry, and formal verification.

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Timaeus (dialogue)

Timaeus (Timaios) is one of Plato's dialogues, mostly in the form of a long monologue given by the title character Timaeus of Locri, written c. 360 BC.

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Timeline of mathematics

This is a timeline of pure and applied mathematics history.

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Topological space

In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.

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Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

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Treasury

A treasury is either.

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Treatise

A treatise is a formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

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Tropical year

A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.

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Tsinghua Bamboo Slips

The Tsinghua Bamboo Slips are a collection of Chinese texts dating to the Warring States period and written in ink on strips of bamboo, that were acquired in 2008 by Tsinghua University, China.

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Tuscany

Tuscany (Toscana) is a region in central Italy with an area of about and a population of about 3.8 million inhabitants (2013).

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Twin prime

A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43).

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Tycho Brahe

Tycho Brahe (born Tyge Ottesen Brahe;. He adopted the Latinized form "Tycho Brahe" (sometimes written Tÿcho) at around age fifteen. The name Tycho comes from Tyche (Τύχη, meaning "luck" in Greek, Roman equivalent: Fortuna), a tutelary deity of fortune and prosperity of ancient Greek city cults. He is now generally referred to as "Tycho," as was common in Scandinavia in his time, rather than by his surname "Brahe" (a spurious appellative form of his name, Tycho de Brahe, only appears much later). 14 December 154624 October 1601) was a Danish nobleman, astronomer, and writer known for his accurate and comprehensive astronomical and planetary observations.

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University of Paris

The University of Paris (Université de Paris), metonymically known as the Sorbonne (one of its buildings), was a university in Paris, France, from around 1150 to 1793, and from 1806 to 1970.

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Upper Paleolithic

The Upper Paleolithic (or Upper Palaeolithic, Late Stone Age) is the third and last subdivision of the Paleolithic or Old Stone Age.

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Utility

Within economics the concept of utility is used to model worth or value, but its usage has evolved significantly over time.

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V. Frederick Rickey

Vincent Frederick Rickey (born 17 December 1941) is an American logician and historian of mathematics.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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Venice

Venice (Venezia,; Venesia) is a city in northeastern Italy and the capital of the Veneto region.

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Victor J. Katz

Victor Joseph Katz (born 31 December 1942, Philadelphia) is an American mathematician, historian of mathematics, and teacher known for using the history of mathematics in teaching mathematics.

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Vietnamese numerals

Historically Vietnamese has two sets of numbers: one is etymologically native Vietnamese; the other uses Sino-Vietnamese vocabulary.

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Vigesimal

The vigesimal or base 20 numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten).

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Vitruvius

Marcus Vitruvius Pollio (c. 80–70 BC – after c. 15 BC), commonly known as Vitruvius, was a Roman author, architect, civil engineer and military engineer during the 1st century BC, known for his multi-volume work entitled De architectura.

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Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

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Warring States period

The Warring States period was an era in ancient Chinese history of warfare, as well as bureaucratic and military reforms and consolidation, following the Spring and Autumn period and concluding with the Qin wars of conquest that saw the annexation of all other contender states, which ultimately led to the Qin state's victory in 221 BC as the first unified Chinese empire known as the Qin dynasty.

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Western world

The Western world refers to various nations depending on the context, most often including at least part of Europe and the Americas.

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William George Horner

William George Horner (9 June 1786 – 22 September 1837) was a British mathematician; he was a schoolmaster, headmaster and schoolkeeper, proficient in classics as well as mathematics, who wrote extensively on functional equations, number theory and approximation theory, but also on optics.

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William of Heytesbury

William of Heytesbury, or William Heytesbury, called in Latin Guglielmus Hentisberus or Tisberus (c. 1313 – 1372/1373), was an English philosopher and logician, best known as one of the Oxford Calculators of Merton College, Oxford, where he was a fellow.

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William Rowan Hamilton

Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.

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Wolfgang Haken

Wolfgang Haken (born June 21, 1928 in Berlin, Germany) is a mathematician who specializes in topology, in particular 3-manifolds.

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World Wide Web

The World Wide Web (abbreviated WWW or the Web) is an information space where documents and other web resources are identified by Uniform Resource Locators (URLs), interlinked by hypertext links, and accessible via the Internet.

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Xu Yue

Xu Yue was a second-century mathematician, born in Donglai, Shandong province in China.

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Yang Hui

Yang Hui (ca. 1238–1298), courtesy name Qianguang (謙光), was a late-Song dynasty Chinese mathematician from Qiantang (modern Hangzhou, Zhejiang).

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YBC 7289

YBC 7289 is a Babylonian clay tablet in the Yale Babylonian Collection, notable for containing an accurate sexagesimal approximation to the square root of 2, the length of the diagonal of a unit square.

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Yuktibhāṣā

Yuktibhāṣā (യുക്തിഭാഷ; "Rationale in the Malayalam/Sanskrit language") also known as Gaṇitanyāyasaṅgraha ("Compendium of astronomical rationale"), is a major treatise on mathematics and astronomy, written by Indian astronomer Jyesthadeva of the Kerala school of mathematics in about AD 1530.

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Zermelo–Fraenkel set theory

In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.

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Zhang Heng

Zhang Heng (AD 78–139), formerly romanized as Chang Heng, was a Han Chinese polymath from Nanyang who lived during the Han dynasty.

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Zhoubi Suanjing

The Zhoubi Suanjing, or Chou Pei Suan Ching (周髀算经), is one of the oldest Chinese mathematical texts.

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Zhu Shijie

Zhu Shijie (1249–1314), courtesy name Hanqing (汉卿), pseudonym Songting (松庭), was one of the greatest Chinese mathematicians living during the Yuan Dynasty.

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Zu Chongzhi

Zu Chongzhi (429–500 AD), courtesy name Wenyuan, was a Chinese mathematician, astronomer, writer and politician during the Liu Song and Southern Qi dynasties.

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0

0 (zero) is both a number and the numerical digit used to represent that number in numerals.

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References

[1] https://en.wikipedia.org/wiki/History_of_mathematics

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