Étienne Bézout was the second son of Pierre Bézout and Jeanne-Hélène Filz. His family was well-connected politically, and both his father and grandfather had served as districtmagistrates, But rather follow in their footsteps, Bézout, who was deeply influenced byLeonhard Euler at an early age, chose to pursue a career inmathematics.[1]At the age of 19 (in 1758), Bézout was elected an adjoint in mechanics of theFrench Academy of Sciences. He got married at the age of 24.[2]
Bézout's marriage at the age of 24 led him to accept the position as a mathematics teacher and examiner of theGardes de la Marine in 1763[2], the post being offered by theDuke of Choiseul. One important task that he was given in this role was to compose a textbook specially designed for teaching mathematics to the naval cadets. One of his most famous works came from this task: theCours de mathématiques à l'usage des Gardes du Pavillon et de la Marine, a four volume work which appeared in 1764-1767. In 1768 Camus, who was the examiner for the artillery, died. Bézout was appointed to succeed him becoming examiner of the Corps d'Artillerie, then, he began work on another mathematics textbook and as a result he producedCours complet de mathématiques à l'usage de la marine et de l'artillerie, a six volume work which appeared between 1770 and 1782. In 1768, Bézout was promoted to associé in mechanics at theAcadémie des Sciences in 1768 and then further promoted to pensionnaire in 1770. Bézout is also acknowledged for his work on algebra, despite being much occupied with his teaching duties, leaving him with little time to relatively little time for algebra research. He published many papers exploring algebraic equations,theory of equations andelimination theory, like theSur plusieurs classes d'équations de tous les degrés qui admettent une solution algébrique, which examined how a single equation in a single unknown could be "attacked" by writing it as two equations in two unknowns. Many of Bézout's papers regardingtheory of equations were gathered and published in possibly his most famous book, theThéorie générale des équations algébriques, published atParis in 1779, which in particular contained much new and valuable matter on thetheory of elimination and symmetrical functions of theroots of an equation: he useddeterminants in a paper in theHistoire de l'académie royale, 1764, but did not treat the general theory.[1]