CALCULUS Understanding Its Concepts and Methods

Augustin Louis Cauchy (1789--1857) --- Historical Sketch

In this book, you first met the name of Cauchy in Chapter 3, where you learned about Cauchy's mean-value theorem As you study more mathematics, you will run across his name in a great many other contexts as well, for he was a very prolific mathematician.

Augustin-Louis Cauchy was born to well-educated parents in 1789 near Paris, very shortly after the beginning of the French Revolution which lasted about ten years, so the Revolution covered and colored his early childhood. And Paris was, so to speak, the center of gravity of that very bloody revolution, which extended a little over ten years. The family moved away from Paris for a while in an attempt to avoid troubles, but life was bleak, and they soon moved back. Friends of Cauchy's father included Joseph Louis Lagrange, and Lagrange took an interest in the boy's mathematical education. This surely must have provided a mathematical springboard for the youngster.

At age 16, Cauchy entered École Polytechnique and two years later transferred to the École des Ponts et Chaussées (School of Bridges and Causeways) to study civil engineering. He worked as an engineer until 1813, when he was 24. While doing his job as an engineer, he continued his mathematics and had proved a theorem about polyhedrons. He also proved that every positive integer is the sum of at most three triangular numbers ( , i.e., numbers of the form ), four square numbers (you know what they are), five pentagonal numbers ( , i.e., numbers of the form ), six hexagonal numbers ( , i.e., numbers of the form ), seven heptagonal numbers ( , i.e., numbers of the form ), eight octagonal numbers ( , i.e., numbers of the form ), and so forth. All of these, and some others among his theorems, are in the field of mathematics called number theory, a branch of the purest form of mathematics. More than this, in 1812, he published an 84-page seminal paper on determinants. Somewhat surprising stuff for an engineer, you surely must agree.

Then in 1815, at age 26, Cauchy was appointed to an assistant professorship at École Polytechnique and the next year won the Grand Prix of the French Academy for his work on waves. At the École, he produced for his students three books on calculus that set the example for calculus books ever since. Through his work, he brought precision and rigor to calculus, as he gave nearly modern definitions of limit, continuity, and convergence. He also contributed to mathematical physics, presenting mathematical treatments of optics and of elasticity theory.

From 1830 to 1848, Cauchy exiled himself from France for political and personal reasons, during which time he travelled throughout Europe, and then was able to return to the École. His contributions to mathematics are voluminous, in both the mathematical and literal sense: his published mathematical works occupy 27 volumes!

Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.