NIELS HENRIK

ABEL (1802-1829)  , Norwegian mathematician, was born at Findoe on the 25th of August 1802 . In 1815 he entered the cathedral school at Christiania, and three years later he gave proof of his mathematical genius by his brilliant solutions of the original problems proposed by B . Holmboe . About this time, his father, a poor Protestant minister, died, and the family was left in straitened circumstances; but a small pension from the state allowed Abel to enter Christiania University in 1821 . His first notable work was a proof of the impossibility of solving the quintic equation by radicals . This investigation was first published in 1824 and in abstruse and difficult form, and afterwards (1826) more elaborately in the first volume of Crelle's Journal . Further state aid enabled him to visit Germany and France in 1825, and having visited the astronomer Heinrich Schumacher (1780-185o) at Hamburg, he spent six months in Berlin, where he became intimate with August Leopold Crelle, who was then about to publish his mathematical journal . This project was warmly encouraged by Abel, who contributed much to the success of the venture . From Berlin he passed to Freiberg, and here he made his brilliant researches h the theory of functions, elliptic, hyperelliptic and a new class known as Abelians being particularly studied . In 1826 he moved to Paris, and during a ten months' stay he met the leading mathematicians of France ; but he was little appreciated, for his work was scarcely known, and his modesty restrained him from pro-claiming his researches . Pecuniary embarrassments, from which he had never been free, finally compelled him to abandon his tour, and on his return to Norway he taught for some time at Christiania . In 1829 Crelle obtained a post for him at Berlin, but the offer did not reach Norway until after his death near Arendal on the 6th of April .

The

early death of this talented mathematician, of whom Legendre said " quelle te"te celle du jeune Norvegien l ", 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 so advanced as to provide mathematicians with numerous ramifications along which progress could be made . 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 . For further details of his mathematical investigations see the articles GROUPS, THEORY OF, and FUNCTIONS OF COMPLEX VARIABLES . See C . A . Bjerknes, Niels Henrik Abel: Tableau de sa vie et son action scientifique (Paris, 1885) ; Lucas de Peslouan, Niels Henrik Abel (Paris, 1906) .