1911 Encyclopædia Britannica/Abel, Niels Henrik

ABEL, NIELS HENRIK (1802–1829), Norwegian mathematician, was born at Findöe 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. Holmboë. 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 (1780–1850) 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 in 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 proclaiming 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 tête 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 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 Holmboë 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).