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Norwegian mathematician who accomplished an amazing amount of brilliant work in his short lifetime. Abel was born on
August 5, 1802 in the small village of Findoe, Norway, where his father was minister in the diocese of Christiansand.
Abel's life was spent in poverty, caused by the large size of his family (he had six brothers and his father died when
he was only eighteen) and the difficult economic situation in Norway at that time. Abel died of tuberculosis at the age
of 26 after being forced to live in miserable conditions because of his inability to obtain a university post.
At the age of 16, Abel gave a proof of the binomial theorem valid for all numbers, extending
Euler's result which had only held for rationals. At age 19, he
showed there is no general algebraic solution for the roots of a quintic equation,
or any general polynomial equation of degree greater than four, in terms of explicit algebraic operations. To
do this, he invented (independently of Galois) an extremely important branch of mathematics known as
group theory, which is invaluable not only in many areas of mathematics, but for much of physics as
well. Among his other accomplishments, Abel wrote a monumental work on elliptic functions which, however, was not discovered until after his death. When asked how he developed his mathematical
abilities so rapidly, he replied "by studying the masters, not their pupils."
Abel sent a paper on the unsolvability of the quintic equation to Gauss, who proceeded to discard
without a glance what he believed to be the worthless work of a crank. In 1825, the Norwegian government funded Abel on
a scholarly visit to France and Germany. Abel then traveled to Paris, where he gave an important paper revealing the
double periodicity of the elliptic functions, which Legendre later
described to Cauchy as "a monument more lasting than bronze" (borrowing a famous sentence by the Roman poet
Horatius). However, Cauchy proceeded to misplace the manuscript. In Berlin, In Berlin, Abel met and was befriended by
August Crelle, an amateur mathematician who had founded the famous Journal für die reine und
angewandte Mathematik (Journal for pure and applied mathematics), which had published several papers by Abel.
However, an offer of a professorship in Berlin was not forthcoming for four years, by which time it was too late. A
letter from Crelle arrived two days after Abel's death, informing his that he had been offered professorship at the
University of Berlin.
Additional biographies: MacTutor (St. Andrews)
Abel, N. H. "Untersuchung der Functionen zweier unabhängig veränderlicher Größen x und y, wie f(x,y), welche die
Eigenschaft haben, daß f(zf(x,y)) eine symmetrische Function von z, x, and y ist." J. reine angew. Math. 1,
11, 1826.
Abel, N. H. "Beweis der Unmöglichkeit, algebraische Gleichungen von höheren Graden als dem vierten allgemein aufzulösen."
J. reine angew. Math. 1, 65-84, 1826.
Abel, N. H. "Bemerkungen über die Abhandlung S. 37 im ersten Hefte dieses Journals (weiter unten No. 161) (von Herrn Kossack
über dir Wirkung einer Kraft auf drei Puncte." J. reine angew. Math. 1, 117, 1826.
Abel, N. H. "Auflösung einer mechanischen Aufgabe." J. reine angew. Math. 1, 153, 1826.
Abel, N. H. "Beweis eines Ausdrucks, von welchem die Binomial-Formel ein einzelner Fall ist." J. reine angew. Math. 1, 159, 1826.
Abel, N. H. "Über die Integration der Differential-Formel
, wenn R und ganze Functionen sind."
J. reine angew. Math. 1, 185, 1826.
Abel, N. H. "Untersuchungen über die Reihe
."
J. reine angew. Math. 1, 311, 1826.
Abel, N. H. "Über einige bestimmte Integrale." J. reine angew. Math. 2, 22, 1827.
Abel, N. H. "Recherches sur les fonctions elliptiques." J. reine angew. Math. 2, 101, 1827.
Abel, N. H. "Über die Functionen, welche Gleichung
genüngten."
J. reine angew. Math. 2, 386, 1827.
Abel, N. H. "Recherches sur les fonctions elliptiques." J. reine angew. Math. 3, 160-190, 1828.
Abel, N. H. "Mémoire sur une classe particulière d'équations résolubles algébriquement." J. reine angew. Math. 4, 131-156, 1829.
Reprinted as Ch. 25 in Abel, N. H. Oeuvres complètes, tome 1. J. Gabay, pp. 478-507, 1992.
Abel, N. H. Oeuvres Completes (Ed. L. Sylow and S. Lie). New York: Johnson Reprint Corp., 1988.
Bell, E. T. "Genius and Poverty: Abel." Ch. 17 in
Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré.
New York: Simon and Schuster, pp. 307-326, 1986.
Ore, Ø. Niels Henrik Abel, Mathematician Extraordinary. New York: Chelsea, 1957.
© 1996-2007 Eric W. Weisstein
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