The Norwegian mathematician Niels Henrik Abel (1802-1829) was born in a family with many children, where all got the basic education by the father. Abel got 1815 into the cathedral school of Kristiania (Oslo), where the mathematics teacher B. M. Holmboe soon saw his genius. Holmboe became a confidant and friend of Abel, and he also published 1839 the first complete edition of Abel's works.

Abel's father died 1820, and Abel maintained himself with scholarships and by giving private lessons. He enrolled 1821 at the university of Kristiania where he got his MA in 1822. The first mathematical texts of Abel date from 1823. In 1824 he printed at his own expense the booklet Mémoire sur les équations algébriques, où l'on démontre l'impossibilité de la solution générale de l'équation du cinquième degré, containing the proof of the impossibility to solve algebraically the general quintic equation.

Abel was awarded a scholarship of Administration for studying two years abroad. In Berlin he got acquainted with A. L. Crelle, who was starting the publishing of his later famed Journal für die reine und angewandte Mathematik. A continual collaboration of Abel with the new journal began. Abel's journey continued via Prague, Vienna and Italy to Paris; here he did not get from French mathematicians the sympathetic response he waited for. Abel's great study on the integrals of algebraic functions, the Abelian integrals, was presented to the French academy of sciences in 1826, but it wasn't published until 1841.

After returning to Norway, where one offered to Abel only some minor temporary posts, he did no more remarkably continue his researches. In April 1829, Crelle had provided to Abel a post of professor in the university of Berlin, but the message reached Abel's home not till two days after Abel's death.

Although Abel starting from childhood had to fight against want, he was able during his short life to create works that had a fundamental significance on several areas of mathematics. For example, the theory of elliptic functions is almost entirely founded by him. Abel's addition theorem is important, too. The notion of algebraic number is due to Abel. He has proved the two-periodicity of the elliptic functions. Abel has studied also the series theory; see e.g. non-existence of universal series convergence criterion, slower divergent series, summation by parts. The greater part of Abel's works were appeared 1839 in Crelle's Journal (e.g. this) by the Norwegian government, and a more complete collection by Ludwig Sylow and Sophus Lie was published in 1881.