ABEL, NIELS HENRIK (18o2--29), Norwegian mathema tician, was born at Findoe, Aug. 25,1802, and educated at Christi ania. His first notable work was a proof of the impossibility of solving the quintic equation by radicals. State aid enabled him to visit Germany and France in 1825. He spent six months in Berlin, where he became intimate with August Leopold Crelle, who was then about to publish his mathematical journal. From Berlin he passed to Freiburg, where he made his brilliant re searches in the theory of elliptical functions. In 1826 he moved to Paris. Want of money finally compelled him to abandon his tour, and on his return to Norway he taught for some time at Christi ania. In 1829 Crelle obtained a post for him at Berlin, but the offer did not reach Norway until after his death near Arendal, April 6.
The early death of this talented mathematician, of whom Legendre said "quelle tete celle du jeune Norvegien!" 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 advanced. 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 L. Sylow and S. Lie was published in 1881.
See C. A. Bjerknes, Niels Henrik Abel: Tableau de sa vie et son action scientifique (1885) ; Lucas de Peslouan, Niels Henrik Abel (1906).