Augustin Cauchy (1789-1857). Caricature of the French mathematician Augustin Cauchy. Cauchy was a pioneer of analysis and the theory of permutation groups. He made numerous contributions to mathematics, including giving modern definitions for limit, continuity and convergence, proving Fermat's three triangle theorem, and work on differential equations, probability and convergence and divergence of infinite series. His output was so prolific that he founded journals solely to publish the results of his research.