Abel , Niels Henrik
(1802–1829) Norwegian mathematician
Abel was born in Froland, the son of a poor pastor; he was educated in mathematics at the University of Christiana (Oslo). After the death of his father, Abel had to support a large family; he earned what he could by private teaching and was also helped out by his teacher. He was eventually given a grant by the Norwegian government to make a trip to France and Germany to visit mathematicians. In Germany he met the engineer and mathematician August Crelle, who was to be of great assistance to him. Crelle published Abel's work and exerted what influence he could to obtain him a post in Germany. Tragically Abel died just when Crelle had succeeded in getting him the chair in mathematics at Berlin.
With Evariste Galois (whom he never met), Abel founded the theory of groups (commutative groups are known as Abelian groups in his honor), and his early death ranks as one of the great tragedies of 19th-century mathematics. One of Abel's first achievements was to solve the longstanding problem of whether the general quintic (of the fifth degree) equation was solvable by algebraic methods. He showed that the general quintic is not solvable algebraically and sent this proof to Karl Gauss, but unfortunately Gauss threw it away unread, having assumed that it was yet another unsuccessful attempt to solve the quintic.
Abel's greatest work was in the theory of elliptic and transcendental functions. Mathematicians had previously focused their attention on problems associated with elliptic integrals. Abel showed that these problems could be immensely simplified by considering the inverse functions of these integrals – the so-called ‘elliptic functions’. He also proved a fundamental theorem,Abel's theorem, on transcendental functions, which he submitted to Augustin Cauchy (and unfortunately fared no better than he did with Gauss). The study of elliptic functions inaugurated by Abel was to occupy many of the best mathematicians for the remainder of the 19th century. He also made very important contributions to the theory of infinite series.

Scientists. . 2011.

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  • Abel, Niels Henrik — ▪ Norwegian mathematician born August 5, 1802, island of Finnøy, near Stavanger, Norway died April 6, 1829, Froland  Norwegian mathematician, a pioneer in the development of several branches of modern mathematics.       Abel s father was a poor… …   Universalium

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  • Niels Henrik Abel — (5 de agosto de 1802 1829), matemático noruego, reconocido por haber probado en 1824 que no hay ninguna fórmula para hallar los ceros de todos los polinomios generales de grados en términos de sus coeficientes y en el de las funciones elípticas,… …   Enciclopedia Universal

  • Niels Henrik Abel — noun Norwegian mathematician (1802 1829) • Syn: ↑Abel, ↑Niels Abel • Instance Hypernyms: ↑mathematician …   Useful english dictionary

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  • ABEL — Selon le Livre de la Genèse, Abel, le berger, était le second fils d’Adam et d’Ève. Il fut tué par son aîné, Caïn, l’agriculteur, son sacrifice ayant été agréé par Dieu et celui de son frère refusé (IV, 1 9). Il semble qu’il ne faille plus… …   Encyclopédie Universelle

  • Abel [4] — Abel, Niels Henrik, norweg. Mathematiker, geb. 5. Aug. 1802 zu Findö im Stift Kristiansand, gest. 6. April 1829 als Dozent an der Universität Kristiania, bes. um die Algebra und die Theorie der elliptischen Funktionen verdient. »Œuvres« (2 Bde.,… …   Kleines Konversations-Lexikon

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