Niels Henrik Abel (August 5, 1802 – April 6, 1829) was a noted Norwegian mathematician who proved the impossibility of solving the quintic equation in radicals.
Abel's life started in poverty and ended in poverty. Abel was born in Nedstrand
, near Finnøy
. Abel was strikingly handsome. His father, Søren Georg Abel, had a degree in theology and philosophy and his grandfather was an active Protestant minister at Gjerstad
. After Abel's grandfather's death, his father was appointed as minister at Gjerstad. When Abel was 13 years old, the long economic crisis in Norway affected Abel's family. In 1815 he entered the Cathedral School
. At first, he was uninspired because the school disappointed Abel, but everything changed when a new mathematics teacher, Bernt Michael Holmboe
, was appointed in 1817. Holmboe saw Abel's talent in mathematics and encouraged him to learn university level mathematics. When his father died in 1820, the family was left in strained circumstances. Holmboe supported Abel with a scholarship to remain at school and raised money from his friends to enable Abel to study at the Royal Frederick University
. Abel entered the university in 1821 and graduated in 1822.
After returning from a visit to Degen
and other mathematicians in Copenhagen
, Abel applied for economic support in order to visit top mathematicians in Germany and France. Instead, he was given funds to stay in Cristiania for two years, and he learned German and French in those years. While learning languages, Abel published his first notable work in 1824, Mémoire sur les équations algébriques ou 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).Abel proved the impossibility of solving the quintic equation
in radicals in 1823 (now referred to as the Abel–Ruffini theorem
). This work was in abstruse and difficult form, in part because the page count was severely restricted in order to save money on printing. A more detailed proof was published in 1826 in the first volume of Crelle's Journal
. In 1825, he was given a government scholarship that enabled him to travel abroad. During the travel, Abel visited the astronomer Heinrich Christian Schumacher
, now a district of Hamburg. He spent six months in Berlin, where he became well acquainted with August Leopold Crelle
, who was then about to publish his mathematical journal. This project was warmly encouraged by Abel, who contributed much to the success of the venture. From Berlin he passed to Freiburg, and here he made his brilliant researches in the theory of functions: elliptic
, and a new class now known as abelian functions
being particularly intensely studied.
In 1826 Abel moved to Paris, and during a ten-month stay he met the leading mathematicians of France; but he was poorly appreciated, as his work was scarcely known, and his modesty restrained him from proclaiming his research. Pecuniary embarrassments, from which he had never been free, finally compelled him to abandon his tour, and on his return to Norway he taught for some time at Christiania.
While in Paris Abel had contracted tuberculosis. For Christmas 1828, Abel travelled by sled to visit his fiancée again in Froland
. He became seriously ill on the journey and despite an improvement which allowed them to enjoy Christmas, he soon became very seriously ill again. Crelle, at the same time, was searching for new job for Abel in Berlin. He successfully managed to appoint Abel as professor of a university and wrote to Abel on the 8 April 1829 to tell him the good news; however, it was too late, as Abel had died two days before.
The early death of this talented mathematician, of whom Adrien-Marie Legendre
said "quelle tête celle du jeune Norvégien!" ("what a head the young Norwegian has!"), cut short a career of extraordinary brilliance and promise. Under Abel's guidance, the prevailing obscurities of analysis 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
, were edited by Holmboe and published in 1839 by the Norwegian government, and a more complete edition by Ludwig Sylow
and Sophus Lie
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" (see abelian group
and abelian category
; also abelian variety
On April 6, 1929, four Norwegian stamps were issued for the centenary of his death. His portrait appears on the 500 kroner banknote (version V) issued during the years 1978–1985. On June 5, 2002, four Norwegian stamps were issued in honour of Abel two months before the bicentenary of his birth. There is a statue of Abel in Oslo. The Abel crater on the Moon was also named in his honour. In 2002, the Abel Prize was established in his honour.