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Augustin Louis Cauchy (August 21, 1789- May 23, 1857) was a French mathematician. He started the
project of formulating and proving the theorems of calculus in a rigorous manner
and was thus an early pioneer of analysis. He also gave
several important theorems in complex analysis and initiated the
study of permutation groups.
Having received his early education from his father Louis Francois Cauchy (1760-1848), who held several minor public appointments and counted Lagrange and Laplace among his
friends, Cauchy entered École Centrale du Pantheon in 1802, and proceeded to the
École Polytechnique 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, where upon 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 of France. 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 College 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'etat 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 Cauchy (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 Eugene Francois
Cauchy (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'Ecole
Polytechnique" (1821); "Le Calcul infinitesimal" (1823); "Lecons sur les applications de calcul infinitesimal"; "La géométrie" (1826-1828); and also in his "Courses of mechanics" (for the École
Polytechnique), "Higher algebra" (for the Faculte des Sciences), and of "Mathematical physics" (for the
College 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 Simeon Poisson.
His collected works, "Oevres complètes d'Augustin Cauchy", have been published in 27 volumes.
See also
External links
(part from the 1911 Encyclopedia)
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