Augustin Louis Cauchy

By: Remi Casier

### Augustin Louis Cauchy

Men pass away, but their deeds abide.

Augustin Louis Cauchy was a French mathematician born on August 21, 1789 in Paris, France. Cauchy was the eldest of all of his siblings and son of Louis Cauchy. Cauchy began an early education from his father and was the particular interest in Lagrange, a visitor to the Cauchy home. In 1802, from the recommendation of Lagrange, Cauchy went to a school where he spent two years studying classical language. In 1805 Cauchy entered a math school and graduated two years later, when he entered an engineering school. After a few short years of an engineer, Augustin Louis decided to devote himself to mathematics. In 1833 Cauchy was summoned by the king Charles X of France to be a tutor for his grandson, and returned home in 1838. Cauchy spent most of his time in the Collège de France, which is a higher education and research establishment, despite several encounters with is strong religious beliefs. Cauchy died May 23, 1857 in Sceaux, France.

Cauchy had influential work in nearly every branch of mathematics, with nearly 800 publications, especially on the theory of functions, integral and differential calculus and algebraic analysis. Cauchy’s first major work occurred in 1805, with the simple solution to the problem of Apollonius. Cauchy continued to solve and generalize many other elegant problems throughout his years. Cauchy gave several important theorems in calculus and complex analysis and began the study of permutation groups.

Perhaps one of Cauchy's most well known theorems is the Cauchy Integral Theorem. The Cauchy Integral Theorem is a complex analysis that states about the line integrals for holomorphic functions in the complex plane.
If $f(z)$ is analytic in some simply connected region, then

(1)
\begin{align} \oint_y f(z)dz=0 \end{align}

For a multiply connected region,

(2)
\begin{align} \oint_{C_1} f(z)dz=\oint_{C_2} f(z)dz \end{align}

Bibliography

O'Connor, JJ (1997, January ). Augustin Louis Cauchy. Retrieved February 25, 2008, from The MacTutor History of Mathematics archive Web site: http://www-history.mcs.st-andrews.ac.uk/Biographies/Cauchy.html

Cauchy, Augustin-Louis, Baron. (2008). In Encyclopædia Britannica. Retrieved February 25, 2008, from Encyclopædia Britannica Web site: http://www.britannica.com/eb/article-9021867

Weisstein, E.W.Cauchy Integral Theorem. Retrieved February 25, 2008, from MathWorld Web site: http://mathworld.wolfram.com/CauchyIntegralTheorem.html