He was homeschooled and became prolific at publishing papers. His major contributions were in analysis, algebra and number theory, and famously developed group theory or the "theory of substitutions" and invented the calculus of residues. He was known for insisting on rigorous proofs.
He was shunned by the mathematical establishment at first, being denied several academic positions and compelled to do his initial work from outside of the university environment. Only after achieving several stunning mathematical insights was he accepted at a faculty position.