French mathematician who provided the rigorous foundations for mathematical analysis — replacing informal reasoning with precise epsilon-delta definitions of limits and continuity.
Rigorous analysis: the Cours d'Analyse (1821) provided the first rigorous treatment of limits, continuity, and derivatives using epsilon-delta definitions. Cauchy sequences: a sequence is Cauchy if its terms eventually become arbitrarily close — this characterizes convergence without reference to a limit. Foundational contributions to complex analysis and group theory.
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