In his In artem analyticum isagoge (Introduction to the Analytical Arts," 1591), François Viète established the letter notation still used in algebra: vowels for unknown quantities or variables, consonants for known quantities or parameters. He wrote a number of other mathematical texts; promoted the use of trigonometry for solving cubic equations; introduced a number of terms, including "coefficient"; and contributed to a variety of other mathematical areas.
The son of Etienne and Marguerite Dupont Viète was born in the French town of Fontenayla-Comte in 1540. By the age of 16, he was studying law at the University of Poitiers, and following his graduation obtained a position as a lawyer in Fontenay. His contacts with royalty and nobility, which would characterize his career, began early: even at this point, Viète could count among his clients Queen Eleanor of Austria and Mary Stuart of Scotland.
From 1564 to 1570, Viète worked for the Soubise family in La Rochelle, eventually leaving his law practice to serve first as private sectary and later as tutor to one of the aristocratic family's daughters. It was probably during this period that he married his first wife, Barbe Cotherau. (After her death, he married Juliette Leclerc; he also had one child.) Also while working with the Soubise family, Viète embraced Protestantism as a member of the Huguenot sect—an extremely risky step in France at that time.
Viète served the French court, and worked in a variety of official capacities, from 1570 to 1584. During this time, he published his first significant mathematical treatise, Canon mathematicus seu ad triangula cum appendibus ("Mathematical Laws Applied to Triangles," 1579.) The text promoted trigonometry, then an underutilized discipline, and made use of all six trigonometric functions.
For five years beginning in 1584, Viète found himself out of favor with King Henry III for his Huguenot sympathies. Given the level of hatred and tension over this issue at the time, it is amazing that he suffered no worse punishment from the Catholic monarchy—and that Henry IV reinstated him on assuming the throne in 1589. Perhaps just to stay on the safe side, Viète rejoined the Catholic Church in 1594.
Several important publications occurred during the years following his reinstatement, beginning with Isagoge, considered by some scholars to be the first algebra textbook of the modern era. In 1593, Viète published Supplementum geometriae, which addressed topics such as the trisection of an angle; the doubling of a cube (a problem that had bedeviled many ancient Greek mathematicians); and the first known explicit statement of π as an infinite product.
With De numerosa in 1600, Viète presented a method for approximating roots of numerical equations. He retired two years later, and died in Paris on December 13, 1603. The posthumous De aquationem recognitione et emedatione libri duo ("Concerning the Recognition and Emendation of Equations," 1615) offered methodology for solving second, third, and fourth degree equations, and contained the first use of the term coefficient.