Augustin-Louis Cauchy

Augustin-Louis Cauchy (1789–1857), a French mathematician, was one of the most important figures in 19th-century mathematics. Raised in a monarchist and religious environment, he was recognised at a very early age by Laplace and Lagrange as an exceptional talent. He entered the École polytechnique at the age of sixteen in 1805, graduated as an engineer in the Corps of Bridges and Roads, and worked in Cherbourg until 1813, when he permanently gave up engineering to devote himself exclusively to mathematics. During the Restoration, he became a professor at the École polytechnique. Refusing to swear allegiance to Louis-Philippe during the Revolution of 1830, he went into exile in Turin, where he was notably involved in educating the young Henri, grandnephew of Charles X. He returned to France in 1838 and regained a position at the École polytechnique. Cauchy's most important contribution to mathematics lies in introducing rigour into analysis: he was the first to formulate precisely the fundamental concepts of limit, continuity, derivative and integral, and to establish rigorous criteria for the convergence of series and sequences. This work, notably collected in his 1821 Cours d'analyse, forms the foundation of modern analysis. Nevertheless, his theory still had gaps, particularly concerning uniform convergence. Furthermore, Cauchy is often criticised for his neglect of the work of Galois and Abel, whose important manuscripts he is said to have misplaced. His work is of considerable scope: he made major contributions to complex analysis, algebra, mechanics and mathematical physics.