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Niels Henrik Abel
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Niels Henrik Abel
Born (1802-08-05)5 August 1802
Nedstrand, Denmark-Norway
Died 6 April 1829(1829-04-06) (aged 26)
Froland, Norway
Nationality Norwegian
Alma mater Royal Frederick University (BA, 1822)
Known for Abel's binomial theorem
Abelian category
Abelian variety
Abel equation
Abel equation of the first kind
Abelian extension
Abel function
Abelian group
Abel's identity
Abel's inequality
Abel's irreducibility theorem
Abel–Jacobi map
Abel–Plana formula
Abel–Ruffini theorem
Abelian means
Abel's summation formula
Abelian and tauberian theorems
Abel's test
Abel's theorem
Abel transform
Abel transformation
Abelian variety
Abelian variety of CM-type
Dual abelian variety
Scientific career
Fields Mathematics
Academic advisors Bernt Michael Holmboe
Niels Henrik Abel signature.png

Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for over 350 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. He made his discoveries while living in poverty and died at the age of 26 from tuberculosis.

Most of his work was done in six or seven years of his working life. Regarding Abel, the French mathematician Charles Hermite said: "Abel has left mathematicians enough to keep them busy for five hundred years." Another French mathematician, Adrien-Marie Legendre, said: "quelle tête celle du jeune Norvégien!" ("what a head the young Norwegian has!").

The Abel Prize in mathematics, originally proposed in 1899 to complement the Nobel Prizes, is named in his honour.

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