**Niels Henrik Abel Biography**

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Niels Henrik Abel (August 5, 1802–April 6, 1829), Norwegian mathematician,
was born in Finnøy. In 1815 he entered the cathedral school at
Christiania (as Oslo was then called), and three years later he
gave proof of his mathematical genius by his brilliant solutions
of the original problems proposed by Bernt 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.

Abel's first notable work was a proof of the impossibility of
solving the quintic equation by radicals (see Abel-Ruffini theorem.)
This investigation was first published in 1824 in abstruse and
difficult form, and afterwards (1826) more elaborately in the
first volume of Crelle's Journal. Further state sponsorship enabled
him to visit Germany and France in 1825, and having visited the
astronomer Schumacher (1780–1850) in Altona near Hamburg he spent
six months in Berlin, where he became well acquainted 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 now known as abelian
functions being particularly intensely studied.

In 1826 Abel moved to Paris, and during a ten month stay he met
the leading mathematicians of France; but he was poorly appreciated,
as his work was scarcely known, and his modesty restrained him
from proclaiming his researchings. 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 early April 1829 Crelle obtained a post for
him in Berlin, but the letter bringing the offer did not reach
Norway until two days after Abel's death from pneumonia at Froland
Ironworks near Arendal.

The early death of this talented mathematician, of whom Legendre
said "quelle tête celle du jeune Norvégien !" ("what a head the
young Norwegian has!"), 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 Ludwig Sylow and Sophus
Lie was published in 1881. The adjective "abelian", derived from
his name, has become so commonplace in mathematical writing that
it is conventionally spelled with a lower-case initial "a" (see
abelian group and abelian category; also abelian variety).

In 2002, the Abel Prize was established in his honour.

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