Augustin-Louis Cauchy
Pioneer of real and complex analysis, prolific mathematician and engineer.
Baron Augustin-Louis Cauchy (21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist. He was among the first to give rigorous statements and proofs for calculus’s key theorems, effectively founding real analysis, and he also broke ground in complex analysis and the study of permutation groups within abstract algebra. His work extended into mathematical physics, especially continuum mechanics. A highly productive scholar, Cauchy wrote roughly eight hundred research articles and five complete textbooks across mathematics and mathematical physics, and his influence on both his contemporaries and later thinkers was substantial, as noted by Hans Freudenthal.
Cauchy was born in Paris just a month after the French Revolution began, which cost his father, a high-ranking police official under the old regime, his job. The family fled to Arcueil during the Reign of Terror, where Cauchy’s father gave him his first lessons. After Robespierre’s fall in 1794, they returned to Paris, and by 1800 his father had secured a bureaucratic post, eventually rising to Secretary-General of the Senate under Napoleon, working directly with Laplace. Mathematician Lagrange was a family friend. On Lagrange’s advice, Cauchy entered the École Centrale du Panthéon in 1802, excelling in Latin and the humanities, but he chose engineering and in 1805 placed second out of 293 applicants for the École Polytechnique. He graduated in 1807 and went on to the École des Ponts et Chaussées, earning top honors in civil engineering.
After school in 1810, Cauchy took a junior engineering post in Cherbourg, working on the Ourcq Canal, the Saint-Cloud Bridge, and the harbor. Despite a busy managerial role, he found time to write three mathematical manuscripts for the Institut de France; two on polyhedra were accepted, but one on conic sections was rejected. In 1812, ill from overwork and losing interest in engineering, he returned to Paris. He stayed on unpaid sick leave for three years, focusing on mathematics—symmetric functions, the symmetric group, and higher-order algebraic equations. He failed three times between 1813 and 1815 to join the Institut de France. After Napoleon’s defeat in 1815, the restored king Louis XVIII re-established the Académie des Sciences in 1816, removing Lazare Carnot and Gaspard Monge for political reasons and appointing Cauchy in their place. This move angered many of his peers, creating lasting enmity.
In November 1815, Cauchy began teaching mathematics at the École Polytechnique, filling in for Louis Poinsot. Around this time he proved Fermat’s polygonal number theorem. He quit engineering and, after the school’s reorganization in 1816, was promoted to full professor. At 28, still living with his parents, his father arranged his marriage in 1818 to Aloise de Bure, a relative of the publisher who issued most of Cauchy’s works. The couple had two daughters, Marie Françoise Alicia (born 1819) and Marie Mathilde (born 1823). Cauchy had two brothers: Alexandre Laurent, a judge, and Eugène François, a publicist who also wrote on mathematics.
- born
- 21 August 1789
- died
- 23 May 1857
- field
- Mathematics, engineering, physics
- nationality
- French
- known_for
- Rigorous foundation of calculus, complex analysis, permutation groups, continuum mechanics
Lore & Background
Cauchy was the son of Louis François Cauchy and Marie-Madeleine Desestre. He had two brothers: Alexandre Laurent Cauchy and Eugene François Cauchy. Cauchy married Aloise de Bure in 1818; they had two daughters, Marie Françoise Alicia (1819) and Marie Mathilde (1823). His father was a highly ranked official in the Parisian police of the Ancien Régime, but lost this position due to the French Revolution. The family survived by escaping to Arcueil, where Cauchy received his first education from his father. After the execution of Robespierre in 1794, they returned to Paris. Louis-François Cauchy became Secretary-General of the Senate, working under Laplace; Lagrange was also a friend. On Lagrange's advice, Cauchy enrolled in the École Centrale du Panthéon in fall 1802. In 1805 he placed second of 293 applicants on the exam for the École Polytechnique and was admitted. He completed the course in 1807 and went on to the École des Ponts et Chaussées, graduating in civil engineering with highest honors. After finishing school in 1810, Cauchy accepted a job as a junior engineer in Cherbourg, where he was assigned the Ourcq Canal project and the Saint-Cloud Bridge project, and worked at the Harbor of Cherbourg. In September 1812 he returned to Paris after becoming ill from overwork. He attempted admission to the First Class of the Institut de France but failed three times between 1813 and 1815. In 1816, after the Académie des Sciences was re-established, the king appointed Cauchy to take the place of one of the removed members. In November 1815, Cauchy began teaching at the École Polytechnique; in 1816 he was promoted to full professor. In 1830, after the July Revolution, Cauchy left France, spending time in Fribourg, Switzerland, then Turin, where he accepted a chair of theoretical physics. In August 1833 he left Turin for Prague to become the science tutor of the Duke of Bordeaux.
Reader's Guide
Cauchy’s mathematical output was immense, comprising roughly eight hundred research articles and five complete textbooks. His work fundamentally reshaped multiple fields: he was among the first to provide rigorous statements and proofs for the core theorems of calculus, thereby establishing real analysis as a formal discipline; he also pioneered complex analysis and made foundational contributions to the study of permutation groups within abstract algebra. Beyond pure mathematics, his investigations extended into mathematical physics, particularly continuum mechanics. His influence on both contemporaries and later mathematicians was profound, as noted by Hans Freudenthal. Cauchy’s career was shaped by his early training as a civil engineer, graduating with highest honors from the École des Ponts et Chaussées, and his subsequent transition from engineering to mathematics after a period of illness and overwork. His election to the Académie des Sciences in 1816, following the removal of Lazare Carnot and Gaspard Monge for political reasons, generated significant resentment among his peers. Despite this, Cauchy became a full professor at the École Polytechnique, where his teaching and research solidified his legacy as a central figure in the rigorous development of modern analysis and algebra.
Did You Know?
- More concepts and theorems have been named for Cauchy than for any other mathematician (in elasticity alone there are sixteen concepts and theorems named for Cauchy).
- Cauchy's first two manuscripts (on polyhedra) were accepted by the Institut de France; the third (on directrices of conic sections) was rejected.
- Cauchy was a notoriously bad lecturer, assuming levels of understanding that only a few of his best students could reach.
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
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