French mathematician who employed rigorous methods of analysis. His prolific output included work on complex functions, determinants, and probability, and on the convergence of infinite series. In calculus, he refined the concepts of the limit and the definite integral.
Cauchy has the credit for 16 fundamental concepts and theorems in mathematics and mathematical physics, more than any other mathematician. His work provided a basis for the calculus. He provided the first comprehensive theory of complex numbers, which contributed to the development of mathematical physics and, in particular, aeronautics.
Cauchy was born in Paris, studied engineering there and worked for a time in construction, then became a professor at the Ecole Polytechnique in 1816 and later at the Collège de France. In 1830 Charles X was overthrown, and, refusing to take the new oath of allegiance, Cauchy went into exile. He became professor of mathematical physics at the University of Turin, and from 1833 he was tutor to Charles X's son in Prague, returning to Paris in 1838 to resume his professorship at the Ecole Polytechnique. In 1843 he published a defence of academic freedom of thought, which was instrumental in the abolition of the oath of allegiance soon after the fall of Louis Philippe in 1848. From 1848 to 1852 Cauchy was a professor at the Sorbonne.
In 1805 Cauchy provided a simple solution to the problem of Apollonius, namely to describe a circle touching three given circles, and in 1816 he published a paper on wave modulation. In mechanics he substituted the concept of the continuity of geometrical displacements for the principle of the continuity of matter and in astronomy he described the motion of the asteroid Pallas.
His main work was published in three treatises: Cours d'analyse de l'Ecole Polytechnique (1821), Résumé des leçons sur le calcul infinitésimal (1823), and Leçons sur les applications de calcul infinitésimal à la géométrie (1826–28).
Cauchy, Augustin Louis
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