# Cauchy, Augustin Louis

## Cauchy, Augustin Louis

Born Aug. 21, 1789, in Paris; died May 23, 1857, in Sceaux. French mathematician. Member of the Paris Academy of Sciences (1816).

Cauchy graduated from the École Polytechnique (1807) and the École des Ponts et Chaussées (1810) in Paris. He worked as an engineer in Cherbourg from 1810 to 1813. From 1816 to 1830 he taught at the École Polytechnique and the Collège de France, and beginning in 1848 at the University of Paris and the Collège de France.

Cauchy's works were devoted to different fields of mathematics (primarily mathematical analysis) and to mathematical physics. His courses on analysis (*Cours d'analyse*, 1821; *Résumé des leçons données à l’école royale polytechnique sur le calcul infinitésimal*, 1823; and *Leçons sur les applications du calculinfinitésimal à la géométric*, vols. 1–2, 1826–28), based on the systematic use of the concept of limit, have served as a model for later courses. In these works he provided a definition of the concept of continuity of a function, a clear construction of the theory of convergent series (Cauchy-Hadamard theorem), and a definition of the integral as a limit of a sum. Cauchy systematically developed the foundations of the theory of analytic functions of a complex variable (*see*), gave an expression for analytic functions in the form of an integral (*see*), provided an expansion of a function in a power series (*see*), and developed the theory of residues.

In the theory of differential equations, Cauchy formulated the so-called Cauchy problem, proved fundamental theorems for the existence of solutions, and developed a method of integration of partial differential equations of the first order (Cauchy's method of characteristics). In his works on the theory of elasticity he regarded a body as a continuous medium and worked with stresses and strains as a function of points. In his works on optics he mathematically worked out FresnePs theory and the theory of dispersion.

In his politics Cauchy was an ultraroyalist, a supporter of the Bourbons (after the revolution of 1830 he was an émigré until 1838), and a clericalist.

### WORKS

*Oeuvres complètes*, series 1, vols. 1–12; Series 2, vols. 1–13. Paris, 1882–1932.

*In Russian translation:*

*Algebraicheskii analiz*. Leipzig, 1864.

*Kratkoe izlozhenie urokov o differentsiarnom i integrarnom ischislenii*. St. Petersburg, 1831.

“Issledovanie o mnogogrannikakh.”

*Uspekhi matematicheskikh nauk*, 1944, issue 10.

### REFERENCES

Bobynin V. V. “Ogiusten Lui Koshi (Ocherk ego zhizni i deiatel’nosti).”*Fiziko-matematicheskie nauki v ikh nastoiashchem i proshedshem*, 1887, vol. 3, nos. 1–3.

Markushevich, A. I.

*Ocherki po istorii teorii analiticheskikh funktsii*. Moscow-Leningrad, 1951.