See also: Abel (homonymy)

Niels Henrik Abel (August 5th 1802 with Frindoë close to Stavanger - April 6th 1829, in Christiana, auj. Oslo) is a Norwegian Mathématicien . He is known for his work in mathematical analysis on the Semi-convergence of the numerical series S, of the continuations and series of functions, the criteria of convergence of Intégrale generalized, on the elliptic concept of Intégrale; in algebra, on the resolution of the equations.

Childhood

Abel, junior by a family of seven children, spent his years of childhood in a country struck by the famine because of the continental Blocus, Napoleon having constrained the crowns of Norway and Denmark to join his coalition against England. His/her father, Sören Georg Abel, educated itself his two oldest sons until 1815, then sent them to the parochial college of Oslo. In this college, Latin, the Greek and the religion were taught with old, with punishments and corporal punishments. The situation developed in 1817 following the reference of a consecutive professor to the death of a pupil: the college recruited a young teacher open to the novel ideas and informed of mathematics, Bernt Michæl Holmboë.

Studies

Holmboë taught the celestial mechanics according to Newton and Lalande. Discovering the interest of Niels Henrik for mathematics, it obtained a purse to him to study at the university (1820). Abel attended this establishment until 1823. At the end of this year, it showed that the unspecified equation of degree five is not resolvable starting from combinations of roots of the coefficients. This work was enough to convince the persons in charge of the university to finance a stay of Abel in Paris, where it could meet, and to perhaps even work with Cauchy. During 1824, Abel thus studied German and French.

Stay in Germany

During the summer 1825, it left for Copenhagen and from there arrived at Altona, where it met Gauss and the astronomer Heinrich Christian Schumacher. The next winter, it is with Berlin where it becomes acquainted with Crelle, which requests its collaboration for a new newspaper of mathematics: the Newspaper of Crelle . In the four months space (November 1825 - February 1826), Abel writes six articles, of which:

• Beweis der Unmöglichkeit DER algebraischen Auflösbarkeit DER allgemeinen Gleichungen , which contains the proof of the impossibility of the equation of the fifth degree by radicals;
• Über die binomische Reihe , where is stated and shown the Critère of sommability of Abel on the semi-convergent series.

In March 1826, Abel leaves Berlin and by Freiberg, Dresden, Vienna and Venice, joined Paris, goal of his voyage, in July.

Disappointment in Paris

Still unknown, Abel does not manage to come into contact with the mathematicians of which it read the books, Adrien-Marie Legendre, Siméon Denis Poisson and Augustin Louis Cauchy. About this last, he writes in Holmboë: “Cauchy cultivates extravagance, it is impossible to get along with him, and yet it is that which knows best how mathematics should be made”. To be made recognize, Abel deposits at the end of October near the Academy of Science a report entitled Recherches on a general property of a very broad class of transcendent functions . This work leads to a general formula to add two elliptic integrals. The rapporteur appointed, Cauchy, impressed by the length of the report and the technicality of the contents, give the reading from there to later. In waiting of an invitation which will not come, Abel can read a new increased edition of the Traité elliptic functions of Legendre. He writes two articles for the Journal of Crelle entitled Recherche on the elliptic functions published in 1827 and 1828. Wearied and with money court, it leaves finally Paris in December 1826.

Last research

From return to Christiana, Abel cannot obtain from stable station at the university, and must accept a work of repeater in a military academy recently created. A few months only after its return, it contracts the Tuberculose. It is at this time that Jacobi publishes its first results on the elliptic integrals: initially a theorem on the rational transformations in these integrals, then a formula of inversion. In May 1828, Abel generalizes the result of Jacobi on the rational transformations. This last is enthusiastic and fact with Legendre the praise of Abel.

At the end of 1828, the health condition of Abel is degraded quickly and it cannot write any more. He dies the next on April 6th.

Abel is at the origin of the algebraic concept of Nombre (solution of a polynomial equation with rational coefficients). He also left many results on the series and the elliptic functions. Abel accepted on a purely posthumous basis the Grand Prix of mathematics of the Institut of France in 1830. He gave his name to the Prix Abel.

Reference

H. Wussing and W. Arnold Biographien bedeutender Mathematikern (1983, 3rd ED.) - VE Verlag Volk und Wissen

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