Abel, Niels Henrik (nēls hĕnˈrĭk äˈbəl) [key], 1802–29, Norwegian mathematician. While a student at the Univ. of Christiania (Oslo) he did fundamental work on the integration of functional expressions and proved the impossiblity of representing a solution of a general equation of fifth degree or higher by a radical expression. He investigated generalizations of the binomial theorem, pioneered in the general theory of elliptic functions, and showed that elliptic functions are a generalization of trigonometric functions. Commutative groups are also called Abelian groups in his honor. He died of tuberculosis at the age of 26, leaving contributions that rank him as one of the greatest mathematicians of the 19th cent.
See O. Ore, Niels Henrik Abel: Mathematician Extraordinary (1957, repr. 1973).
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