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Abel's first notable work was a proof of the impossibility of solving the quintic equation by radicals (see Abel-Ruffini theorem.) This investigation was first published in 1824 in abstruse and difficult form, and afterwards (1826) more elaborately in the first volume of Crelle's Journal. Further state sponsorship enabled him to visit Germany and France in 1825, and having visited the astronomer Schumacher (1780-1850) in Altona near 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 Freiberg, and here he made his brilliant researches in the theory of functions: ellipticIn complex analysis, an elliptic function is, roughly speaking, a function defined on the complex plane which is periodic in two directions. The elliptic functions can be seen as analogs of the trigonometric functions (which have a single period only)., hyperelliptic, and a new class now known as abelian functions being particularly intensely studied.
In 1826 Abel moved to ParisEiffel Tower has become the symbol of Paris throughout the world. Paris is the capital and largest city of France. The city is built on an arc of the River Seine, and is thus divided into two parts: the Right Bank to the north and the smaller Left Bank to, 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 researchings. 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. In early April 1829 Crelle obtained a post for him in Berlin, but the letter bringing the offer did not reach Norway until two days after Abel's death from pneumoniaPneumonia is defined as an infection involving the alveoli of the lungs. It occurs in patients of all age groups, but young children and the elderly, as well as immunocompromised and immune deficient patients, are especially at risk. Causal therapy is wit at Froland Ironworks near ArendalGeneral The town Arendal (N 58 27, E 8 56 ) in the county of Aust-Agder, Norway, has 39,554 inhabitants as of January 1, 2002. Area: 272 km². It is the administrative center of Aust-Agder county. In the end of the 19th century Arendal was a major shipping.
The early death of this talented mathematician, of whom LegendreAdrien-Marie Legendre ( September 18 1752 January 10 1833) was a French mathematician. He made important contributions to statistics, number theory, abstract algebra and mathematical analysis. Most of his work was brought to perfection by others: his work 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 Swedish 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).
In 2002, the Abel Prize was established in his honour.