Though he conducted important research in algebraic equations, Etienne Bézout is remembered primarily for his contributions to mathematics education. Most notable was Cours de mathematiques, a six-volume textbook that arose from his work as teacher for the French military, and which in turn influenced the teaching of mathematics on both sides of the Atlantic.
The second son of Pierre and Helene Filz Bézout, Etienne Bézout was born on March 31, 1739, in Nemours, France. His family was well-connected politically, and both his father and grandfather had served as district magistrates. Rather than follow in their footsteps, however, Bézout—who at an early age was deeply influenced by Leonhard Euler (1707-1783)—chose a career in mathematics.
At the age of 19, Bézout became an adjunct member of the Académie Royale des Sciences, and 10 years later was elected to full membership. Much of his work was distinctly practical in nature, a fact that arose partly from his marriage at the age of 24: with a family to support, Bézout availed himself of the steady income offered by a position as teacher and examiner to naval cadets in the Gardes du Pavillon et de la Marine. Five years later, in 1768, he began working with artillery officer candidates as well.
These teaching responsibilities required that Bézout eschew a theoretical approach in favor of a practical one, and as a result he developed a highly understandable course of study. This became the basis for the six-volume Cours de mathematiques: A l'usage des Gardes du Pavillon est de la Marine, which became an enormously popular textbook. Over the years that followed, it would reach the United States, where it became a favored text at both Harvard University and West Point Military Academy.
Many observers admired Bézout for his simplification of difficult subjects, and for preserving the important discoveries of such recent mathematicians as Euler and Jean le Rond d'Alembert (1717-1783). Other commentators, however, faulted Bézout for what they regarded as a simplistic approach to the discipline. In fact Bézout himself can hardly be dismissed as a mathematical lightweight: during the 1760s, he devoted himself to challenging questions involving determinants in algebraic equations, and particularly to elimination theory.
Bézout died in 1783 in Basses-Loges, France, but his influence extended far into the next century. Cours de mathematiques, the English edition of which saw numerous reprints, remained an important text in America; meanwhile, Bézout's work had an impact on the mathematician Gaspard Monge (1746-1818), the military leader Lazare Carnot (1753-1823), and others.