# 1911 Encyclopædia Britannica/Cauchy, Augustin Louis

**CAUCHY, AUGUSTIN LOUIS**, Baron (1780–1857), French
mathematician, was born at Paris on the 21st of August 1789,
and died at Sceaux (Seine) on the 23rd of May 1857. Having
received his early education from his father Louis François
Cauchy (1760–1848), who held several minor public appointments
and counted Lagrange and Laplace among his friends,
Cauchy entered École Centrale du Panthéon in 1802, and
proceeded to the École Tolytechnique in 1805, and to the École
des Ponts et Chaussées in 1807. Having adopted the profession
of an engineer, he left Paris for Cherbourg in 1810, but returned
in 1813 on account of his health, whereupon Lagrange and
Laplace persuaded him to renounce engineering and to devote
himself to mathematics. He obtained an appointment at the
École Polytechnique, which, however, he relinquished in 1830
on the accession of Louis Philippe, finding it impossible to take
the necessary oaths. A short sojourn at Freiburg in Switzerland
was followed by his appointment in 1831 to the newly-created
chair of mathematical physics at the university of Turin. In
1833 the deposed king Charles X. summoned him to be tutor to
his grandson, the duke of Bordeaux, an appointment which
enabled Cauchy to travel and thereby become acquainted with
the favourable impression which his investigations had made.
Charles created him a baron in return for his services. Returning
to Paris in 1838, he refused a proffered chair at the Collège de
France, but in 1848, the oath having been suspended, he resumed
his post at the École Polytechnique, and when the oath was
reinstituted after the *coup d’état* of 1851, Cauchy and Arago
were exempted from it. A profound mathematician, Cauchy
exercised by his perspicuous and rigorous methods a great
influence over his contemporaries and successors. His writings
cover the entire range of mathematics and mathematical physics.

Cauchy had two brothers: Alexandre Laurent (1792–1857), who became a president of a division of the court of appeal in 1847, and a judge of the court of cassation in 1849; and Eugène François (1802–1877), a publicist who also wrote several mathematical works.

The genius of Cauchy was promised in his simple solution of the
problem of Apollonius, *i.e.* to describe a circle touching three given
circles, which he discovered in 1805, his generalization of Euler’s
theorem on polyhedra in 1811, and in several other elegant problems.
More important is his memoir on wave-propagation which obtained
the *Grand Prix* of the Institut in 1816. His greatest contributions
to mathematical science are enveloped in the rigorous methods which
he introduced. These are mainly embodied in his three great
treatises, *Cours d’analyse de l’École Polytechnique* (1821); *Le Calcul*
*infinitésimal* (1823); *Leçons sur les applications du calcul infinitésimal*
*a la géométrie* (1826–1828); and also in his courses of mechanics (for
the École Polytechnique), higher algebra (for the Faculté des
Sciences), and of mathematical physics (for the Collège de France).
His treatises and contributions to scientific journals (to the number
of 789) contain investigations on the theory of series (where he
developed with perspicuous skill the notion of convergency), on the
theory of numbers and complex quantities, the theory of groups and
substitutions, the theory of functions, differential equations and
determinants. He clarified the principles of the calculus by developing
them with the aid of limits and continuity, and was the first
to prove Taylor’s theorem rigorously, establishing his well-known
form of the remainder. In mechanics, he made many researches,
substituting the notion of the continuity of geometrical displacements
for the principle of the continuity of matter. In optics, he
developed the wave theory, and his name is associated with the simple
dispersion formula. In elasticity, he originated the theory of stress,
and his results are nearly as valuable as those of S. D. Poisson. His
collected works, *Œuvres complètes d’Augustin Cauchy*, have been
published in 27 volumes.

See C. A. Valson, *Le Baron Augustin Cauchy: sa vie et ses travaux*
(Paris, 1868).