Augustin-Louis Cauchy

Lore & Background

Cauchy was born in Paris one month after the French Revolution. His father, a former police official, lost his position and the family fled to Arcueil, where Cauchy received his first education. After the Reign of Terror, they returned to Paris, and his father became Secretary-General of the Senate under Napoleon, working directly under Laplace. On the advice of Lagrange, Cauchy enrolled in the École Centrale du Panthéon, winning prizes in Latin and the humanities, but chose an engineering career. He entered the École Polytechnique in 1805, graduating in 1807, and then the École des Ponts et Chaussées, graduating with highest honors in civil engineering.

After school, Cauchy worked as a junior engineer in Cherbourg on the Ourcq Canal, Saint-Cloud Bridge, and the Harbor of Cherbourg. Despite a busy managerial job, he prepared three mathematical manuscripts; two on polyhedra were accepted, one on conic sections was rejected. In 1812, ill from overwork, he returned to Paris and eventually left engineering for mathematics. He failed three times to enter the First Class of the Institut de France, but in 1816, after the restoration, King Louis XVIII appointed him to replace Lazare Carnot or Gaspard Monge, causing resentment among peers. He married Aloïse de Bure in 1818; they had two daughters.

In 1830, the July Revolution led Cauchy to leave France in exile, refusing to swear allegiance to the new regime. He lost all positions except his academy membership. He taught in Turin from 1832–1833, then moved to Prague in 1833 to tutor the exiled Duke of Bordeaux, a task he undertook seriously but with little success, as the Duke had no interest in mathematics.

Reader's Guide

Cauchy's significance lies in his foundational contributions to multiple branches of mathematics. He was one of the first to rigorously state and prove the key theorems of calculus, effectively creating real analysis. He pioneered complex analysis and advanced the study of permutation groups in abstract algebra. In mathematical physics, he contributed notably to continuum mechanics. Hans Freudenthal noted that more concepts and theorems have been named for Cauchy than for any other mathematician, with sixteen in elasticity alone. Cauchy was extremely prolific, writing approximately eight hundred research articles and five complete textbooks. His work influenced contemporaries and successors profoundly, though his rigid political and religious views led to exile and strained relationships with peers. His legacy endures in the many theorems, concepts, and methods that bear his name across analysis, algebra, and physics.

Did You Know?

• Cauchy wrote approximately eight hundred research articles and five complete textbooks.
• He was one of the first to rigorously state and prove the key theorems of calculus, creating real analysis.
• Hans Freudenthal stated that more concepts and theorems have been named for Cauchy than for any other mathematician.
• Cauchy lost all his positions in Paris after refusing to swear an oath of allegiance to the new regime following the July Revolution of 1830.

Notable Quotes (Wikiquote)

"Residues arise … naturally in several branches of analysis … . Their consideration provides simple and easy-to-use methods, which are applicable to a large number of diverse questions, and some new results … ." — Augustin-Louis Cauchy "... très souvent les lois particulières déduites par les physiciens d'un grand nombre d'observations ne sont pas rigoureuses, mais approchées." — Augustin-Louis Cauchy "... very often the laws derived by physicists from a large number of observations are not rigorous, but approximate." — Augustin-Louis Cauchy "Augustin Louis Cauchy (1868). Sept leçons de physique. Bureau du Journal Les Mondes. p. 15." — Augustin-Louis Cauchy