The New International Encyclopædia/Cauchy, Augustin Louis

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CAUCHY, kṓ'shḗ', Augustin Louis (1789-1857). A French mathematician. He was born in Paris, and was educated at the Ecole Polytechnique. In 1810 he went to Cherbourg, in the capacity of an engineer, but his health failing, he returned to Paris in 1813, renounced engineering, and chose pure science for his life work. His Mémoire sur la théorie des ondes was crowned by the Institute in 1815, and in 1816 he became a member of the Academy of Sciences. Later he became professor at the Polytechnic School. In 1830 he refused to take the oath required by Louis Philippe, and went into voluntary exile. During his stay abroad he held for a short time the chair of mathematics in Turin, and later (1834) went to Prague as tutor of the Comte de Chambord. He returned to France in 1837, but his political views were such as to bar him from the higher professorships until the advent of the Government of 1848. In that year Cauchy was made professor of mathematical astronomy at the Sorbonne, a chair which he held, with a brief interruption, until his death. In politics Cauchy was a Legitimist. He was known as a man of piety and was a defender of the Jesuits.

The works of Cauchy occupy a leading place in science. All parts of pure and applied mathematics, as geometry, algebra, the theory of numbers, integral calculus, mechanics, astronomy, and mathematical physics, are indebted to his discoveries. He verified the periodicity of elliptic functions, gave the first impetus to the general theory of functions, contributed to determinants (q.v.), and laid the foundation for the modern treatment of the convergence of infinite series (q.v.). He emphasized the imaginary as a fundamental, not subsidiary, quantity, perfected the method of integration of linear differential equations (see Calculus), advanced the theory of substitutions, invented the calculus of residues, and, in general, was one of the leaders of the Nineteenth Century in infusing vigor into analysis. The propagation of light and the theory of elasticity also received his attention.

Consult: Valson, La Vie et les travaux de Cauchy (Paris, 1868); Terquem, “Analyse des travaux de Cauchy,” in the Nouvelles annales de mathématiques (Paris, 1857). Les œvres completes d'Augustin Cauchy (Paris, 1882-1901) were published under the direction of the Academy of Sciences.