Mathematician:Niels Henrik Abel

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Norwegian mathematician who died tragically young.

Made significant contributions towards algebra, analysis and group theory.

Best known for proving the impossibility of solving the general quintic in radicals (Abel-Ruffini Theorem).

Due to a series of administrative mishaps and personal blunders by various influential mathematicians, he was not recognised for what he was until too late.

An important influence on the founding of Crelle's Journal, the first volume for which he contributed several papers.

He was finally appointed to a chair of mathematics in Berlin, but by that time he had died of tuberculosis at the age of $26$.




  • Born: 5 Aug 1802, Frindöe (near Stavanger), Norway
  • 1815: Sent to the Cathedral School in Christiania (now Oslo) with his older brother
  • 1817: Became a pupil of Bernt Holmboe
  • 1820: Death of Abel's father
  • 1821: Enter University of Christiania with assistance from Bernt Holmboe
  • 1822: Graduated
  • 1826: Went to Paris
  • Died: 6 April 1829, Froland, Norway

Theorems and Definitions


Definitions of concepts named for Niels Henrik Abel can be found here.


Results named for Niels Henrik Abel can be found here.


  • 1823 (?): Solutions of some problems by means of definite integrals
  • 1826: Beweis eines Ausdruckes, von welchem die Binomial-Formel ein einzelner Fall ist. (J. reine angew. Math. Vol. 1: pp. 159 – 160)
  • 1827: Recherches sur les fonctions elliptiques

Notable Quotes

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils.

My eyes have been opened in the most surprising manner. If you disregard the very simplest cases, there is in all of mathematics not a single infinite series whose sum has been rigorously determined. In other words, the most important parts of mathematics stand without a foundation. It is true that most of it is valid, but that is very surprising. I struggle to find a reason for it, an exceedingly interesting problem.

Critical View

Abel has left mathematicians enough to keep them busy for $500$ years.
-- Charles Hermite

All of Abel's works carry the imprint of an ingenuity and force of thought which is amazing. One may say that he was able to penetrate all obstacles down to the very foundations of the problem, with a force of thought which appeared irresistible ... He distinguished himself equally by the purity and nobility of his character and by a rare modesty which made his person cherished to the same unusual degree as was his genius.
-- August Leopold Crelle

Abel, the lucky fellow! He has done something everlasting! His ideas will always have a fertilizing influence on our science.
-- Karl Weierstrass