Niels Henrik Abel (1802-1829) was a son of a Norwegian clergyman. He died of tuberculosis, unemployed and starving.
Despite his short life, Abel is famous for his work on group theory (Abelian groups), polynomial equations, real analysis and elliptic functions (Abelian integrals). In 1826, he wrote to his teacher B. M. Holmboe,
Divergent series are the invention of the devil, and it is shameful to base on them any demonstration whatsoever.
This did not stop him from introducing a method of summation of divergent series, Abel summation.
The importance of Abel’s work was recognised after his death, and today the Abel Prize is one of the most valuable awards in mathematics, worth around 750 000 Euros. It is not at all clear what Abel would have thought about this.