Niels Henrik Abel ( , ; 5 August 1802 – 6 April 1829) was a Norwegian

Niels Henrik Abel – utdypning (NBL-artikkel)

– Store norske leksion Niels Henrik Abel's father, Søren Georg Abel, had a degree in

Groups.dcs.st-and.ac.uk. Retrieved on 2011-07-12. This led to a discovery in 1823 that a solution to a fifth- or higher-degree equation was impossible. Abel graduated in 1822. His performance was exceptionally high in mathematics and average in other matters.

File:NOK 500 V recto.jpg, Niels Henrik Abel on a Norwegian 500 kroner banknote, 1978
File:Abelmonumentet 1.jpg, Statue of Niels Henrik Abel, called the "Abelmonumentet", in Oslo (former Christiania) by Gustav Vigeland.
File:Abelmonumentet av Vigeland. - no-nb digifoto 20150625 00154 NB MIT FNR 11682.jpg, Abelmonumentet in front of the
File:Stamps of Norway, 1929-Niels Henrik Abel1.jpg
File:Stamps of Norway, 1929-Niels Henrik Abel2.jpg
File:Stamps of Norway, 1929-Niels Henrik Abel3.jpg
File:Stamps of Norway, 1929-Niels Henrik Abel4.jpg

Biographies and handwritten manuscripts

from the Abel Prize website *

* *

Translation of Niels Henrik Abel's "Research on Elliptic Functions"

a

Convergence

Famous Quotes by Niels Henrik Abel

a

Convergence

The Niels Henrik Abel mathematical contest

The Norwegian Mathematical Olympiad

Family genealogy

* {{DEFAULTSORT:Abel, Niels Henrik 1802 births 1829 deaths 19th-century deaths from tuberculosis 19th-century Norwegian mathematicians Group theorists Norwegian Lutherans Norwegian mathematicians People educated at Oslo Cathedral School People from Froland Tuberculosis deaths in Norway University of Oslo alumni

mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation
In algebra, a quintic function is a function (mathematics), function of the form
:g(x)=ax^5+bx^4+cx^3+dx^2+ex+f,\,
where , , , , and are members of a field (mathematics), field, typically the rational numbers, the real numbers or the complex ...

in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for over 250 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. He made his discoveries while living in poverty and died at the age of 26 from tuberculosis
Tuberculosis (TB) is an infectious disease usually caused by ''Mycobacterium tuberculosis'' (MTB) bacteria. Tuberculosis generally affects the lungs, but it can also affect other parts of the body. Most infections show no symptoms, in ...

.
Most of his work was done in six or seven years of his working life. Regarding Abel, the French mathematician Charles Hermite
Charles Hermite () Royal Society of London, 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, ...

said: "Abel has left mathematicians enough to keep them busy for five hundred years." Another French mathematician, Adrien-Marie Legendre
Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials
In physical science and mathemati ...

, said: "What a head the young Norwegian has!"
The Abel Prize
The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. ...

in mathematics, originally proposed in 1899 to complement the Nobel Prize
The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel#Nobel Prize, Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest ben ...

s (but first awarded in 2003), is named in his honour.
Life

Early life

Niels Henrik Abel was born inNedstrand
Nedstrand (locally, ''Stranda'') is a village in Tysvær municipality in Rogaland county, Norway. The village is on the Nedstrand peninsula's southeast coast, at the confluence of the Nedstrandsfjorden and Vindafjorden. The village of Hindaråv ...

, Norway, as the second child of the pastor Søren Georg Abel and Anne Marie Simonsen. When Niels Henrik Abel was born, the family was living at a rectory on Finnøy. Much suggests that Niels Henrik was born in the neighboring parish, as his parents were guests of the bailiff
A bailiff (from Middle English baillif, Old French ''baillis'', ''bail'' "custody") is a manager, overseer or custodian – a legal officer to whom some degree of authority or jurisdiction is given. Bailiffs are of various kinds and their offi ...

in Nedstrand in July / August of his year of birth.
Stubhaug, ArildNiels Henrik Abel – utdypning (NBL-artikkel)

– Store norske leksion Niels Henrik Abel's father, Søren Georg Abel, had a degree in

theology
Theology is the systematic study of the nature of the Divinity, divine and, more broadly, of religious belief. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itself with the ...

and philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

and served as pastor at Finnøy. Søren's father, Niels's grandfather, Hans Mathias Abel, was also a pastor, at Gjerstad Church near the town of Risør. Søren had spent his childhood at Gjerstad, and had also served as chaplain there; and after his father's death in 1804, Søren was appointed pastor at Gjerstad and the family moved there. The Abel family originated in Schleswig
The Duchy of Schleswig ( da, Hertugdømmet Slesvig; german: Herzogtum Schleswig; nds, Hartogdom Sleswig; frr, Härtochduum Slaswik) was a duchy in Southern Jutland () covering the area between about 60 km (35 miles) north and 70 km ( ...

and came to Norway in the 17th century.
Anne Marie Simonsen was from Risør; her father, Niels Henrik Saxild Simonsen, was a tradesman and merchant ship-owner, and said to be the richest person in Risør. Anne Marie had grown up with two stepmothers, in relatively luxurious surroundings. At Gjerstad rectory, she enjoyed arranging balls and social gatherings. Much suggests she was early on an alcoholic and took little interest in the upbringing of the children. Niels Henrik and his brothers were given their schooling by their father, with handwritten books to read. An addition table in a book of mathematics reads: 1+0=0.
Cathedral School and Royal Frederick University

With Norwegian independence and the first election held in Norway, in 1814, Søren Abel was elected as a representative to theStorting
The Storting ( no, Stortinget ) (lit. the Great Thing (assembly), Thing) is the supreme legislature of Norway, established in 1814 by the Constitution of Norway. It is located in Oslo. The Unicameralism, unicameral parliament has 169 members and ...

. Meetings of the Storting were held until 1866 in the main hall of the Cathedral School
Cathedral schools began in the Early Middle Ages as centers of advanced education, some of them ultimately evolving into medieval universities. Throughout the Middle Ages and beyond, they were complemented by the monastic schools. Some of these e ...

in Christiania (now known as Oslo
Oslo ( , , or ; sma, Oslove) is the Capital city, capital and List of towns and cities in Norway, most populous city of Norway. It constitutes both a Counties of Norway, county and a Municipalities of Norway, municipality. The municipality o ...

). Almost certainly, this is how he came into contact with the school, and he decided that his eldest son, Hans Mathias, should start there the following year. However, when the time for his departure approached, Hans was so saddened and depressed over having to leave home that his father did not dare send him away. He decided to send Niels instead.
In 1815, Niels Abel entered the Cathedral School at the age of 13. His elder brother Hans joined him there a year later. They shared rooms and had classes together. Hans got better grades than Niels; however, a new mathematics teacher, Bernt Michael Holmboe
Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are conc ...

, was appointed in 1818. He gave the students mathematical tasks to do at home. He saw Niels Henrik's talent in mathematics, and encouraged him to study the subject to an advanced level. He even gave Niels private lessons after school.
In 1818, Søren Abel had a public theological argument with the theologian Stener Johannes Stenersen regarding his catechism
A catechism (; from grc, 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 c ...

from 1806. The argument was well covered in the press. Søren was given the nickname "Abel Treating" ''( Norwegian: "Abel Spandabel")''. Niels' reaction to the quarrel was said to have been "excessive gaiety". At the same time, Søren also almost faced impeachment after insulting Carsten Anker, the host of the Norwegian Constituent Assembly
The Norwegian Constituent Assembly (in Norwegian ''Grunnlovsforsamlingen'', also known as ''Riksforsamlingen'') is the name given to the 1814 Constituent assembly, constitutional assembly at Eidsvoll in Norway, that adopted the Norwegian Constitu ...

; and in September 1818 he returned to Gjerstad with his political career in ruins. He began drinking heavily and died only two years later, in 1820, aged 48.
Bernt Michael Holmboe supported Niels Henrik Abel with a scholarship to remain at the school and raised money from his friends to enable him to study at the Royal Frederick University.
When Abel entered the university in 1821, he was already the most knowledgeable mathematician in Norway. Holmboe had nothing more he could teach him and Abel had studied all the latest mathematical literature in the university library. During that time, Abel started working on the quintic equation
In algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost ...

in radicals. Mathematicians had been looking for a solution to this problem for over 250 years. In 1821, Abel thought he had found the solution. The two professors of mathematics in Christiania, Søren Rasmussen and Christopher Hansteen, found no errors in Abel's formulas, and sent the work on to the leading mathematician in the Nordic countries, Carl Ferdinand Degen in Copenhagen. He too found no faults but still doubted that the solution, which so many outstanding mathematicians had sought for so long, could really have been found by an unknown student in far-off Christiania. Degen noted, however, Abel's unusually sharp mind, and believed that such a talented young man should not waste his abilities on such a "sterile object" as the fifth degree equation, but rather on elliptic function
In the mathematical field of complex analysis, elliptic functions are a special kind of Meromorphic function, meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integral ...

s and transcendence; for then, wrote Degen, he would "discover Magellanian thoroughfares to large portions of a vast analytical ocean". Degen asked Abel to give a numerical example of his method. While trying to provide an example, Abel found a mistake in his paper.Abel biographyGroups.dcs.st-and.ac.uk. Retrieved on 2011-07-12. This led to a discovery in 1823 that a solution to a fifth- or higher-degree equation was impossible. Abel graduated in 1822. His performance was exceptionally high in mathematics and average in other matters.

Career

After he graduated, professors from university supported Abel financially, and Professor Christopher Hansteen let him live in a room in the attic of his home. Abel would later view Ms. Hansteen as his second mother. While living here, Abel helped his younger brother, Peder Abel, through examen artium. He also helped his sister Elisabeth to find work in the town. In early 1823, Niels Abel published his first article in "Magazin for Naturvidenskaberne", Norway's first scientific journal, which had been co-founded by Professor Hansteen. Abel published several articles, but the journal soon realized that this was not material for the common reader. In 1823, Abel also wrote a paper in French. It was "a general representation of the possibility to integrate all differential formulas" ('' Norwegian: en alminnelig Fremstilling af Muligheten at integrere alle mulige Differential-Formler)''. He applied for funds at the university to publish it. However, the work was lost while being reviewed, never to be found thereafter. In mid-1823, Professor Rasmussen gave Abel a gift of 100 speciedaler so he could travel toCopenhagen
Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

and visit Ferdinand Degen and other mathematicians there. While in Copenhagen, Abel did some work on 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 number, positive integers , , and satisfy the equation for any integer value of greater than 2. The cases ...

. Abel's uncle, Peder Mandrup Tuxen, lived at the naval base in Christianshavn
Christianshavn (literally, "ingChristian's Harbour") is a neighbourhood in Copenhagen
Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter ...

, Copenhagen, and at a ball there Niels Abel met Christine Kemp, his future fiancée. In 1824, Christine moved to Son, Norway to work as a governess and the couple got engaged over Christmas.
After returning from Copenhagen, Abel applied for a government scholarship in order to visit top mathematicians in Germany and France, but he was instead granted 200 speciedaler yearly for two years, to stay in Christiania and study German and French. In the next two years, he was promised a scholarship of 600 speciedaler yearly and he would then be permitted to travel abroad. While studying these languages, Abel published his first notable work in 1824, ''Mémoire sur les équations algébriques où on démontre l'impossibilité de la résolution de l'équation générale du cinquième degré'' (Memoir on algebraic equations, in which the impossibility of solving the general equation of the fifth degree is proven). By 1823, Abel had at last proved the impossibility of solving the quintic equation in radicals (now referred to as the Abel–Ruffini theorem
In mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in m ...

). However, this paper was in an abstruse and difficult form, in part because he had restricted himself to only six pages in order to save money on printing. A more detailed proof was published in 1826 in the first volume of ''Crelle's Journal
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal
In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research.
Co ...

''.
In 1825, Abel wrote a personal letter to King Carl Johan of Norway/Sweden requesting permission to travel abroad. He was granted this permission, and in September 1825 he left Christiania together with four friends from university (Christian P.B Boeck, Balthazar M. Keilhau, Nicolay B. Møller and Otto Tank). These four friends of Abel were traveling to Berlin and to the Alps to study geology. Abel wanted to follow them to Copenhagen and from there make his way to Göttingen. The terms for his scholarship stipulated that he was to visit Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

in Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...

and then continue to Paris. However, when he got as far as Copenhagen, he changed his plans. He wanted to follow his friends to Berlin instead, intending to visit Göttingen and Paris afterwards.
On the way, he visited the astronomer Heinrich Christian Schumacher in Altona, now a district of Hamburg. He then spent four months in Berlin, where he became well acquainted with August Leopold Crelle, who was then about to publish his mathematical journal, '' Journal für die reine und angewandte Mathematik''. This project was warmly encouraged by Abel, who contributed much to the success of the venture. Abel contributed seven articles to it in its first year.
From Berlin Abel also followed his friends to the Alps. He went to Leipzig
Leipzig ( , ; Upper Saxon: ) is the most populous city in the Germany, German States of Germany, state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's L ...

and Freiberg
Freiberg is a college town, university and former mining town in Saxony, Germany. It is a so-called ''Große Kreisstadt'' (large county town) and the administrative centre of Mittelsachsen district.
Its historic town centre has been placed un ...

to visit Georg Amadeus Carl Friedrich Naumann and his brother the mathematician August Naumann. In Freiberg Abel did research in the theory of functions, particularly, elliptic
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

, hyperelliptic, and a new class now known as abelian functions.
From Freiberg they went on to Dresden, Prague, Vienna, Trieste, Venice, Verona, Bolzano, Innsbruck, Luzern and Basel. From July 1826 Abel traveled on his own from Basel to Paris. Abel had sent most of his work to Berlin to be published in Crelle's Journal, but he had saved what he regarded as his most important work for the French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

, a theorem on addition of algebraic differentials. With the help of a painter, Johan Gørbitz, he found an apartment in Paris and continued his work on the theorem. He finished in October 1826 and submitted it to the academy. It was to be reviewed by Augustin-Louis Cauchy
Baron
Baron is a rank of nobility
Nobility is a social class found in many societies that have an aristocracy (class), aristocracy. It is normally ranked immediately below Royal family, royalty. Nobility has often been an Estates o ...

. Abel's work was scarcely known in Paris, and his modesty restrained him from proclaiming his research. The theorem was put aside and forgotten until his death.
Abel's limited finances finally compelled him to abandon his tour in January 1827. He returned to Berlin, and was offered a position as editor of Crelle's Journal, but opted out. By May 1827 he was back in Norway. His tour abroad was viewed as a failure. He had not visited Gauss in Göttingen and he had not published anything in Paris. His scholarship was therefore not renewed and he had to take up a private loan in Norges Bank
Norges Bank / Noregs Bank is the central bank of Norway. The bank shall promote economic stability in Norway. Norges Bank also manages the Government Pension Fund of Norway and the bank’s own foreign exchange reserves.
History
The history of ...

of 200 spesidaler. He never repaid this loan. He also started tutoring. He continued to send most of his work to Crelle's Journal. But in mid-1828 he published, in rivalry with Carl Jacobi, an important work on elliptic functions in ''Astronomische Nachrichten
''Astronomische Nachrichten'' (''Astronomical Notes''), one of the first international journals in the field of astronomy, was established in 1821 in science, 1821 by the German astronomer Heinrich Christian Schumacher. It claims to be the oldest a ...

'' in Altona.
Death

While in Paris, Abel contractedtuberculosis
Tuberculosis (TB) is an infectious disease usually caused by ''Mycobacterium tuberculosis'' (MTB) bacteria. Tuberculosis generally affects the lungs, but it can also affect other parts of the body. Most infections show no symptoms, in ...

. At Christmas 1828, he traveled by sled to Froland
Froland is a List of municipalities of Norway, municipality in Agder counties of Norway, county, Norway. It is part of the Districts of Norway, traditional region of Southern Norway, Sørlandet. The administrative center is the village of Blakst ...

, Norway, to visit his fiancée. He became seriously ill on the journey. Although a temporary improvement allowed the couple to enjoy the holiday together, he died relatively soon after on 6 April 1829, just two days before a letter arrived from August Crelle. Crelle had been searching for a new job for Abel in Berlin and had actually managed to have him appointed as a Professor at the University of Berlin
Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin
Berlin ( , ) is the capital and largest city of Germany ...

. Crelle wrote to Abel to tell him, but the good news came too late.
Contributions to mathematics

Abel showed that there is no general algebraic solution for the roots of aquintic equation
In algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost ...

, or any general polynomial equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form
:P = 0
where ''P'' is a polynomial with coefficients in some field (mathematics), field, often the field of the rational numbers. For many authors, the term '' ...

of degree greater than four, in terms of explicit algebraic operations. To do this, he invented (independently of Galois) a branch of mathematics known as group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

, which is invaluable not only in many areas of mathematics, but for much of physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...

as well. Abel sent a paper on the unsolvability of the quintic equation to Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

, who proceeded to discard without a glance what he believed to be the worthless work of a crank.
As a 16-year-old, Abel gave a rigorous proof of the binomial theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial into a sum involving terms of the form , where th ...

valid for all numbers, extending Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

's result which had held only for rationals
In mathematics, a rational number is a number that can be expressed as the quotient or fraction (mathematics), fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ) ...

. Abel wrote a fundamental work on the theory of elliptic integrals, containing the foundations of the theory of elliptic functions.
While travelling to Paris he published a paper revealing the double periodicity of elliptic functions, which Adrien-Marie Legendre
Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials
In physical science and mathemati ...

later described to Augustin-Louis Cauchy
Baron
Baron is a rank of nobility
Nobility is a social class found in many societies that have an aristocracy (class), aristocracy. It is normally ranked immediately below Royal family, royalty. Nobility has often been an Estates o ...

as "a monument more lasting than bronze" (borrowing a famous sentence by the Roman poet Horatius). The paper was, however, misplaced by Cauchy.
While abroad Abel had sent most of his work to Berlin to be published in the ''Crelle's Journal'', but he had saved what he regarded as his most important work for the French Academy of Sciences, a theorem on addition of algebraic differentials. The theorem was put aside and forgotten until his death. While in Freiberg, Abel did research in the theory of functions, particularly, elliptic
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

, hyperelliptic, and a new class now known as abelian functions.
In 1823 Abel wrote a paper titled "a general representation of the possibility to integrate all differential formulas" ( Norwegian: ''en alminnelig Fremstilling af Muligheten at integrere alle mulige Differential-Formler''). He applied for funds at the university to publish it. However the work was lost, while being reviewed, never to be found thereafter.
Abel said famously of Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

's writing style, "He is like the fox, who effaces his tracks in the sand with his tail." Gauss replied to him by saying, "No self-respecting architect leaves the scaffolding in place after completing his building."
Legacy

Under Abel's guidance, the prevailing obscurities ofanalysis
Analysis (plural, : analyses) is the process of breaking a complexity, complex topic or Substance theory, substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics a ...

began to be cleared, new fields were entered upon and the study of functions so advanced as to provide mathematicians with numerous ramifications along which progress could be made. His works, the greater part of which originally appeared in ''Crelle's Journal
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal
In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research.
Co ...

'', were edited by Bernt Michael Holmboe and published in 1839 by the Norwegian government, and a more complete edition by Ludwig Sylow
Peter Ludwig Mejdell Sylow () (12 December 1832 – 7 September 1918) was a Norway, Norwegian mathematician who proved foundational results in group theory. Biography
He was born and died in Oslo, Christiania (now Oslo). Sylow was a son of govern ...

and Sophus Lie
Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899) was a Norwegian mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians ...

was published in 1881. The adjective "abelian", derived from his name, has become so commonplace in mathematical writing that it is conventionally spelled with a lower-case initial "a" (e.g., abelian group
In mathematics, an abelian group, also called a commutative group, is a group (mathematics), group in which the result of applying the group Operation (mathematics), operation to two group elements does not depend on the order in which they are w ...

, abelian category, and abelian variety
In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a Algebraic variety#Projective variety, projective algebraic variety that is also an algebraic group, i.e., has a group law th ...

).
On 6 April 1929, four Norwegian stamps were issued for the centenary of Abel's death. His portrait appears on the 500- kroner banknote
A banknote—also called a bill ( North American English), paper money, or simply a note—is a type of negotiable promissory note, made by a bank
A bank is a financial institution that accepts deposits from the public and creates ...

(version V) issued during 1978–1985. On 5 June 2002, four Norwegian stamps were issued in honour of Abel two months before the bicentenary of his birth. There is also a 20-kroner coin issued by Norway in his honour. A statue of Abel stands in Oslo, and crater Abel
Abel ''Hábel''; ar, هابيل, Hābīl is a Biblical figure in the Book of Genesis within Abrahamic religions. He was the younger brother of Cain, and the younger son of Adam and Eve, the first couple in Biblical history. He was a shepherd wh ...

on the Moon
The Moon is Earth's only natural satellite. It is the List of natural satellites, fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth ( ...

was named after him. In 2002, the Abel Prize
The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. ...

was established in his memory.
Mathematician 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 ...

wrote about Abel:
Royal Palace, Oslo
The Royal Palace ( no, Slottet or ''Det kongelige slott'') in Oslo was built in the first half of the 19th century as the Norwegian residence of the France, French-born Charles XIV John, King Charles III John, who reigned as king of Union betwee ...

File:Holmengard-119.JPG, Niels Henrik Abel memorial in Gjerstad
File:Abelmonument.jpg, A monument for Abel at Frolands verk by Gustav Lærum
See also

* List of things named after Niels Henrik Abel *Évariste Galois
Évariste Galois (; ; 25 October 1811 – 31 May 1832) was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by Nth root, ...

Notes

References

Further reading

* *External links

Biographies and handwritten manuscripts

from the Abel Prize website *

* *

Translation of Niels Henrik Abel's "Research on Elliptic Functions"

a

Convergence

Famous Quotes by Niels Henrik Abel

a

Convergence

The Niels Henrik Abel mathematical contest

The Norwegian Mathematical Olympiad

Family genealogy

* {{DEFAULTSORT:Abel, Niels Henrik 1802 births 1829 deaths 19th-century deaths from tuberculosis 19th-century Norwegian mathematicians Group theorists Norwegian Lutherans Norwegian mathematicians People educated at Oslo Cathedral School People from Froland Tuberculosis deaths in Norway University of Oslo alumni