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Abel, Neils Henrik

theory elliptic crelle degree

[ ah bel] (1802–29) Norwegian mathematician: pioneer of group theory; proved that no algebraic solution of the general fifth-degree equation exists.

Abel was the son of a Lutheran minister. In 1821 he went to Oslo to study at the university, but his father’s death forced him to give this up in order to support the large family of which he was the eldest; he was extremely poor throughout his life. In 1825 he visited Germany and France and with Leopold Crelle (1780–1855) founded Crelle’s Journal in which much of his work was published, since Abel could not persuade the French Académie des Sciences to do so. Having failed to find a university post in Germany, and with his health failing due to tuberculosis, he returned to Norway, where he died shortly afterwards aged 26. Two days later a letter from Crelle announced that the professorship of mathematics at Berlin, one of the most prestigious posts in the world, had been awarded to him.

Despite his tragically early death Abel largely founded the theory of groups, and in particular commutative groups, which were later known as Abelian groups. He also showed that the general fifth-degree equation is not solvable algebraically (ironically threw this proof away unread when Abel sent it to him). He revolutionized the important area of elliptic integrals with his theory of elliptic and transcendental functions, and contributed to the theory of infinite series.

Abendroth,Hermann [next] [back] Abel,Carl Friedrich

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