Mathematician:Niels Henrik Abel

Mathematician
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, 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 $26$.

Nationality
Norwegian

History

 * 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
 * 1820: Death of Abel's father
 * 1821: Enter University of Christiania with assistance from
 * 1822: Graduated
 * 1826: Went to Paris
 * Died: 6 April 1829, Froland, Norway

Definitions

 * Abelian Function
 * Abelian Group
 * Abelian Integral
 * Abel's Integral Equation
 * Abelian Mean
 * Abel's Mechanical Problem
 * Abel's Series
 * Abel Summation Method
 * Abel Summability
 * Abelian Theorem

Results

 * Abel's Generalisation of Binomial Theorem
 * Abel's Lemma, also known as Abel's Transformation and Abel's Partial Summation Formula
 * Abel's Limit Theorem
 * Abel's Test
 * Abel's Test for Uniform Convergence
 * Abel's Theorem
 * Abel-Ruffini Theorem (with )

Publications

 * 1823 (?): Solutions of some problems by means of definite integrals


 * 1824: (Memoir on algebraic equations, in which the impossibility of solving the general equation of the fifth degree is proven)




 * 1826: (lost by  for years and not published till $1841$)


 * 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.


 * 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.


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