Background
Étienne Bézout was born on March 31, 1730, in Nemours, Île-de-France, France, the second son of Pierre Bezout and Hélène-Jeanne Filz. Both his father and grandfather had held the office of magistrate in the town of Nemours.
Académie des sciences, 23 Quai de Conti, 75270 Paris, France
In 1758, Étienne Bézout became a member of the Académie des sciences.
(This book provides the first English translation of Bézou...)
This book provides the first English translation of Bézout's masterpiece, the General Theory of Algebraic Equations. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail.
https://www.amazon.com/General-Theory-Algebraic-Equations-Etienne-ebook/dp/B002WJM5S2/ref=sr_1_2?keywords=%C3%89tienne+B%C3%A9zout&qid=1558446548&s=gateway&sr=8-2
1779
mathematician scientist teacher
Étienne Bézout was born on March 31, 1730, in Nemours, Île-de-France, France, the second son of Pierre Bezout and Hélène-Jeanne Filz. Both his father and grandfather had held the office of magistrate in the town of Nemours.
Although his father hoped Étienne would succeed him, the young man was strongly drawn to mathematics, particularly through reading the works of Leonhard Euler.
In 1758 Bézout was appointed an adjoint in mechanics of the Académie des Sciences and, in the same year, as a royal censor. He was appointed examiner of the Gardes de la Marine in 1763, the post being offered to him by the Duke of Choiseul. One important task that he was given in this role was to compose a textbook specially designed for teaching mathematics to the students.
Bézout is famed for the textbooks which came out of this assignment. The first was Cours de mathématiques à l'usage des Gardes du Pavillon et de la Marine, a four-volume work which appeared in 1764 - 1767.
In 1763, the due de Choiseul offered Bezout a position as teacher and examiner in mathematical science for young would-be naval officers, the Gardes du Pavillon et de la Marine.
In 1768 Camus, who was the examiner for the artillery, died and Bézout was appointed to succeed him becoming examiner of the Corps d'Artillerie. He began work on another mathematics textbook and as a result he produced Cours complet de mathématiques à l'usage de la marine et de l'artillerie, a six-volume work which appeared between 1770 and 1782. This was a very successful textbook and for many years it was the book which students hoping to enter the École Polytechnique studied.
As might be expected given this approach aiming at the readership for whom Bézout intended his texts, his books came in for a certain amount of criticism for lacking rigour. However, despite this, they were books which could be understood by those who needed to use mathematics and as a result were very popular and widely used. Their use spread beyond France for they were translated into English and used in North America. In particular, Harvard University adopted them as calculus textbooks.
Returning to give more information about Bézout's career, it should be noted that he was promoted to associé in mechanics at the Académie des Sciences in 1768 and then further promoted to pensionnaire in 1770.
As it was indicated Bézout is famed for being a writer of textbooks but he is famed also for his work on algebra, in particular on equations. He was much occupied with his teaching duties after his 1763 appointments and he took these very seriously indeed. As a consequence, he could devote relatively little time to research and he made a conscience decision to restrict the range of his work so that he could produce worthwhile results in a narrow order.
The way Bézout went about his research is interesting since still today it is a good approach for obtaining results. He attacked quite general problems, but since an attack was usually beyond what could be achieved with the mathematical knowledge then available, he attacked special cases of the general problems which he could solve. This approach often leads slowly to more and more understanding of the general case which may eventually become soluble. Bézout had a name for this approach to mathematics, namely the "method of simplifying assumptions".
His first paper on the theory of equations Sur plusieurs classes d'équations de tous les degrés qui admettent une solution algébrique examined how a single equation in a single unknown could be attacked by writing it as two equations in two unknowns.
Hereinafter Bézout made the simplifying assumption that one of the two equations was of a particularly simple form. For example, he considered the case when one of the two equations had only two terms, the term of degree n and a constant term. Already this paper had introduced the topic to which Bézout would make his most important contributions, namely methods of elimination to produce from a set of simultaneous equations, a single resultant equation in one of the unknowns.
He also did important work on the use of determinants in solving equations. This appears in a paper Sur le degré des équations résultantes de l'évanouissement des inconnues which he published in 1764. As a result of the ideas in this paper for solving systems of simultaneous equations, Sylvester, in 1853, called the determinant of the matrix of coefficients of the equations the Bézoutiant.
These and further papers published by Bézout in the theory of equations were gathered together in Théorie générale des équations algébraiques which was published in 1779. This work includes a result known as Bézout's theorem.
Étienne Bézout died on September 27, 1783, in Avon, Île-de-France, France.
(This book provides the first English translation of Bézou...)
1779
Although Étienne Bézout was reserved and somewhat somber in society, those who knew him well spoke of his great kindness and warm heart.