The Mozart of Mathematics — Niels Henrik Abel

 

“Although Abel shared with many mathematicians a complete lack of musical talent, I will not sound absurd if I compare his kind of productivity and his personality with Mozart’s.” — Felix Klein

Niels Henrik Abel (1802–1829) died at age 26. Largely self-taught, in his short life the young Abel made pioneering contributions to variety of subjects in pure mathematics, including: algebraic equations, elliptic functions, elliptic integrals, functional equations, integral transforms and series representations. Born on the small island of Finnøy in Rogaland, Norway, the early years of Abel’s short life was dominated by the instability of an alcoholic father who died when he was 16 years old.

More or less self-taught, at 21, Abel provided the first complete proof demonstrating that there is no general algebraic solution for the roots of a quintic equation, or any general polynomial equation of degree greater than four. At that point, the problem had been unresolved for over 250 years. In the process of writing the proof, he laid the foundation — independently of Galois — for the branch of mathematics now known as group theory. At 22, he also wrote a fundamental work on elliptic integrals which helped lay the foundation for what would later be the theory of elliptic functions. Then, on April 6th 1829, at the age of 26, Abel died of tuberculosis. He had contracted the disease while in Paris and gotten ill while travelling by sled to the south of Norway in December to visit his fiancée.

Unbelievably, for the duration of his brief life he was never able to attain a permanent research or teaching position. Living hand-to-mouth from scholarships, temporary teaching positions and various patrons, at the time of his death he was working to repay the debts of his family in abject poverty. In the ultimate cruel irony, not two days after he passed a letter arrived from August Crelle (1780–1855) (of Crelle’s Journal) announcing that had been appointed Professor at the University of Berlin.

This is the story of Niels Henrik Abel, the Mozart of Mathematics. Estimated reading time is 30 minutes. For the occasion, recommended mood music is Requiem, K. 626: Lacrimosa, available on Spotify or YouTube.

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