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. The July Revolution of 1830 resulted in the imposition of an oath of allegiance to French King Louis-Philippe, which Cauchy refused to do and lost his academic posts as a result. But in 1838 he was restored to his professorship at the École Polytechnique.