Abel: The Mozart of Mathematics

“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 the modest age of 26 years old. 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 fundament…