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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. [1]

100 relations: Abel (crater), Abel equation, Abel equation of the first kind, Abel Prize, Abel transform, Abel's binomial theorem, Abel's identity, Abel's inequality, Abel's irreducibility theorem, Abel's summation formula, Abel's test, Abel's theorem, Abel–Jacobi map, Abel–Plana formula, Abel–Ruffini theorem, Abelian and tauberian theorems, Abelian category, Abelian extension, Abelian group, Abelian variety, Abelian variety of CM-type, Adrien-Marie Legendre, Algebraic equation, Algebraic function, Analysis, Astronomische Nachrichten, August Leopold Crelle, Augustin-Louis Cauchy, Évariste Galois, Bailiff, Banknote, Bernt Michael Holmboe, Binomial theorem, Carl Ferdinand Degen, Carl Friedrich Gauss, Carl Gustav Jacob Jacobi, Carsten Anker, Catechism, Charles Hermite, Charles XIV John of Sweden, Christianshavn, Christopher Hansteen, Copenhagen, Crelle's Journal, Denmark–Norway, Divergent series, Dual abelian variety, Duchy of Schleswig, Elliptic function, Elliptic integral, ... Expand index (50 more) »

## Abel (crater)

Abel is an ancient lunar impact crater that lies near the southeast limb of the Moon's near side.

## Abel equation

The Abel equation, named after Niels Henrik Abel, is a type of functional equation which can be written in the form or, equivalently, and controls the iteration of.

## Abel equation of the first kind

In mathematics, an Abel equation of the first kind, named after Niels Henrik Abel, is any ordinary differential equation that is cubic in the unknown function.

## Abel Prize

The Abel Prize (Abelprisen) is a Norwegian prize awarded annually by the Government of Norway to one or more outstanding mathematicians.

## Abel transform

In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions.

## Abel's binomial theorem

Abel's binomial theorem, named after Niels Henrik Abel, is a mathematical identity involving sums of binomial coefficients.

## Abel's identity

In mathematics, Abel's identity (also called Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation.

## Abel's inequality

In mathematics, Abel's inequality, named after Niels Henrik Abel, supplies a simple bound on the absolute value of the inner product of two vectors in an important special case.

## Abel's irreducibility theorem

In mathematics, Abel's irreducibility theorem, a field theory result described in 1829 by Niels Henrik Abel, asserts that if &fnof;(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of &fnof;(x).

## Abel's summation formula

In mathematics, Abel's summation formula, introduced by Niels Henrik Abel, is intensively used in number theory to compute series.

## Abel's test

In mathematics, Abel's test (also known as Abel's criterion) is a method of testing for the convergence of an infinite series.

## Abel's theorem

In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients.

## Abel–Jacobi map

In mathematics, the Abel–Jacobi map is a construction of algebraic geometry which relates an algebraic curve to its Jacobian variety.

## Abel–Plana formula

In mathematics, the Abel–Plana formula is a summation formula discovered independently by and.

## 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.

## Abelian and tauberian theorems

In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named after Niels Henrik Abel and Alfred Tauber.

## Abelian category

In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties.

## Abelian extension

In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian.

## Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

## Abelian variety

In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions.

## Abelian variety of CM-type

In mathematics, an abelian variety A defined over a field K is said to have CM-type if it has a large enough commutative subring in its endomorphism ring End(A).

Adrien-Marie Legendre (18 September 1752 – 10 January 1833) was a French mathematician.

## 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.

## Algebraic function

In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation.

## Analysis

Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it.

## Astronomische Nachrichten

Astronomische Nachrichten (Astronomical Notes), one of the first international journals in the field of astronomy, was founded in 1821 by the German astronomer Heinrich Christian Schumacher.

## August Leopold Crelle

August Leopold Crelle (17 March 1780 &ndash; 6 October 1855) was a German mathematician.

## 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.

## Évariste Galois

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

## Bailiff

A bailiff (from Middle English baillif, Old French baillis, bail "custody, charge, office"; cf. bail, based on the adjectival form, baiulivus, of Latin bajulus, carrier, manager) is a manager, overseer or custodian; a legal officer to whom some degree of authority or jurisdiction is given.

## Banknote

A banknote (often known as a bill, paper money, or simply a note) is a type of negotiable promissory note, made by a bank, payable to the bearer on demand.

## Bernt Michael Holmboe

Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician.

## Binomial theorem

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

## Carl Ferdinand Degen

Carl Ferdinand Degen (1 November 1766 – 8 April 1825) was a Danish mathematician.

## 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.

## Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory.

## Carsten Anker

Carsten Tank Anker (17 November 1747 – 13 March 1824) was a Norwegian businessman, civil servant, politician and one of the Fathers of the Constitution of Norway.

## Catechism

A catechism (from κατηχέω, "to teach orally") is a summary or exposition of doctrine and serves as a learning introduction to the Sacraments traditionally used in catechesis, or Christian religious teaching of children and adult converts.

## Charles Hermite

Prof Charles Hermite FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.

## Charles XIV John of Sweden

Charles XIV and III John or Carl John, (Swedish and Norwegian: Karl Johan; 26 January 1763 – 8 March 1844) was King of Sweden (as Charles XIV John) and King of Norway (as Charles III John) from 1818 until his death, and served as de facto regent and head of state from 1810 to 1818.

## Christianshavn

Christianshavn is a neighbourhood in Copenhagen, Denmark.

## Christopher Hansteen

Christopher Hansteen (26 September 1784 – 11 April 1873) was a Norwegian geophysicist, astronomer and physicist, best known for his mapping of Earth's magnetic field.

## Copenhagen

Copenhagen (København; Hafnia) is the capital and most populous city of Denmark.

## Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

## Denmark–Norway

Denmark–Norway (Danish and Norwegian: Danmark–Norge or Danmark–Noreg; also known as the Oldenburg Monarchy or the Oldenburg realms) was an early modern multi-national and multi-lingual real unionFeldbæk 1998:11 consisting of the Kingdom of Denmark, the Kingdom of Norway (including Norwegian overseas possessions the Faroe Islands, Iceland, Greenland, et cetera), the Duchy of Schleswig, and the Duchy of Holstein.

## 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.

## Dual abelian variety

In mathematics, a dual abelian variety can be defined from an abelian variety A, defined over a field K.

## Duchy of Schleswig

The Duchy of Schleswig (Hertugdømmet Slesvig; Herzogtum Schleswig; Low German: Sleswig; North Frisian: Slaswik) was a duchy in Southern Jutland (Sønderjylland) covering the area between about 60 km north and 70 km south of the current border between Germany and Denmark.

## Elliptic function

In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions.

## Elliptic integral

In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse.

## Examen artium

Examen artium was the name of the academic certification conferred in Denmark and Norway, qualifying the student for admission to university studies.

## Felix Klein

Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.

## 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.

## Finnøy

Finnøy is an island municipality in Rogaland county, Norway.

## Freiberg

Freiberg is a university and mining town in the Free State of Saxony, Germany.

The French Academy of Sciences (French: Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research.

## Froland

Froland is a municipality in Aust-Agder county, Norway.

## Göttingen

Göttingen (Low German: Chöttingen) is a university city in Lower Saxony, Germany.

## Georg Amadeus Carl Friedrich Naumann

Georg Amadeus Carl Friedrich Naumann (30 May 1797 &ndash; 26 November 1873), also known as Karl Friedrich Naumann, was a German mineralogist and geologist.

Gjerstad is a municipality in Aust-Agder county, Norway.

## Heinrich Christian Schumacher

Prof Heinrich Christian Schumacher FRS(For) FRSE (September 3, 1780 – December 28, 1850) was a German-Danish astronomer and mathematician.

## History of group theory

The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads.

## Horace

Quintus Horatius Flaccus (December 8, 65 BC – November 27, 8 BC), known in the English-speaking world as Horace, was the leading Roman lyric poet during the time of Augustus (also known as Octavian).

## Humboldt University of Berlin

The Humboldt University of Berlin (Humboldt-Universität zu Berlin, abbreviated HU Berlin), is a university in the central borough of Mitte in Berlin, Germany.

## Hyperelliptic curve

In algebraic geometry, a hyperelliptic curve is an algebraic curve given by an equation of the form where f(x) is a polynomial of degree n > 4 with n distinct roots.

## Johan Gørbitz

Johan Görbitz (8 September 1782 – 3 July 1853) was a Norwegian painter.

## Leipzig

Leipzig is the most populous city in the federal state of Saxony, Germany.

## 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.

## List of things named after Niels Henrik Abel

This is the list of things named after Niels Henrik Abel (1802 – 1829), a Norwegian mathematician.

## Mathematical proof

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

## Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

## Mathematics

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

## Moon

The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite.

## Nedstrand

Nedstrand (locally, Stranda) is a village in Tysvær municipality in Rogaland county, Norway.

## Nobel Prize

The Nobel Prize (Swedish definite form, singular: Nobelpriset; Nobelprisen) is a set of six annual international awards bestowed in several categories by Swedish and Norwegian institutions in recognition of academic, cultural, or scientific advances.

## Norges Bank

Norges Bank / Noregs Bank is the central bank of Norway.

## Norwegian Constituent Assembly

The Norwegian Constituent Assembly (in Norwegian Grunnlovsforsamlingen, also known as Riksforsamlingen) is the name given to the 1814 Constitutional Assembly at Eidsvoll in Norway, that voted the Norwegian Constitution and formalised the dissolution of the union with Denmark.

## Norwegian krone

The krone (sign: kr; code: NOK), plural kroner, is the currency of Norway and its dependent territories.

## Norwegian rigsdaler

The rigsdaler was the unit of currency used in Norway until 1816 and in Denmark until 1873.

## Oslo

Oslo (rarely) is the capital and most populous city of Norway.

## Oslo Cathedral School

Schola Osloensis, known in Norwegian as Oslo katedralskole (Oslo Cathedral School) and more commonly as "Katta" is a selective upper secondary school located in Oslo, Norway.

## Peter Ludwig Mejdell Sylow

Peter Ludwig Mejdell Sylow (12 December 1832 – 7 September 1918) was a Norwegian mathematician who proved foundational results in group theory.

## Philosophy

Philosophy (from Greek φιλοσοφία, philosophia, literally "love of wisdom") is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language.

## Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

## Quintic function

In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.

## Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

## Risør (town)

Risør is a town and the administrative centre of Risør municipality in Aust-Agder county, Norway.

## Søren Georg Abel

Søren Georg Abel (3 January 1772 – 5 May 1820) was a Norwegian priest and politician, also known as the father of mathematician Niels Henrik Abel.

## Son, Norway

Son is an old town, and a former municipality.

## Sophus Lie

Marius Sophus Lie (17 December 1842 – 18 February 1899) was a Norwegian mathematician.

## Stepfamily

A stepfamily, blended family, or bonus family is a family where at least one parent has children that are not genetically related to the other spouse or partner.

## Storting

The Storting (Stortinget, "the great thing" or "the great assembly") is the supreme legislature of Norway, established in 1814 by the Constitution of Norway.

## Summation by parts

In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums.

## Theology

Theology is the critical study of the nature of the divine.

## Transcendental number theory

Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with integer coefficients), in both qualitative and quantitative ways.

## Tuberculosis

Tuberculosis (TB) is an infectious disease usually caused by the bacterium Mycobacterium tuberculosis (MTB).

## Union between Sweden and Norway

Sweden and Norway or Sweden–Norway (Svensk-norska unionen; Den svensk-norske union), officially the United Kingdoms of Sweden and Norway, or as the United Kingdoms, was a personal union of the separate kingdoms of Sweden and Norway under a common monarch and common foreign policy that lasted from 1814 until its amicable and peaceful dissolution in 1905.

## University of Oslo

The University of Oslo (Universitetet i Oslo), until 1939 named the Royal Frederick University (Det Kongelige Frederiks Universitet), is the oldest university in Norway, located in the Norwegian capital of Oslo.