Day 79 · Mar 19

Birthday of Augustin-Louis Cauchy (1789)

One of history's most prolific mathematicians with 789 papers — the most in mathematics before Euler. Cauchy put calculus on rigorous foundations, introducing the formal ε-δ definitions of limits, continuity, and convergence still used today. He proved the fundamental theorem of algebra (imperfectly — Gauss gave the first complete proof), founded complex analysis, and made foundational contributions to mechanics and optics. He was also deeply religious and politically conservative — refusing to swear oaths of loyalty to successive French governments cost him his academic positions.

Before Cauchy's ε-δ definition, mathematicians used 'infinitesimals' — infinitely small quantities. What was wrong with this approach, and how does ε-δ fix it?

Practice related topics on DuelMath

Challenge someone →