This entry contributed by Margherita Barile

A non-professional French mathematician, also known under the latinized name of Vieta, who disclosed the way to modern symbolic algebra. He had a very brilliant legal career starting in his hometown Fontenay-le-Comte as the private lawyer of a noble family, and ended up as a personal counselor of King Henri III.

His first mathematical works were two books of trigonometric tables (Canon Mathematicus, and Universalium Inspectionum Liber Singularis, 1579) where the values of sines were computed with a (startling) accuracy of 10^-8.

Viète's major contribution is his innovative treatment of algebraic equations. He initiated the systematical use of letters to denote both the coefficients and the unknowns: this was the beginning of a new type of algebra, expressed in terms of abstract formulas and general rules, instead of the geometric visualizations, the text problems and the numerical examples used by his predecessors back since antiquity. He, however, payed some sort of tribute to the ancient tradition by refusing negative solutions, by sticking to the use of words to denote powers (the exponents would be introduced by Descartes one generation later), and by keeping a terminology inspired by areas and volumes ("plane" and "solid" for the product of two or three numbers respectively).

His treatise Isagoge in Artem Analyticem (1591) is a presentation of his mathematical project. There he introduces the basic notation and gives the rules for the product of powers and the equivalent transformation of equations in a way that calls to mind the first pages of Diophantus' Arithmetica. Viète's classification of the branches of algebra is also partially derived from Greek mathematics: he distinguishes between zetetics (translating a problem into an equation), poristics (proving theorems through equations), and exegetics or rhetics (solving equations). His main works (Ad Logisticem Speciosam Notae Priores, 1631; Zeteticorum Libri Quinque, 1591 or 1593; De Aequationem Recognitione et Emendatione Tractatus Duo, 1615) are entirely devoted to the study of the general properties of algebraic equations. In another treatise, De Numerosa Potestatum ad Exegesin Resolutione (1600), he presented techniques for the numerical computation of roots. He also wrote three minor works on angle sections and other constructions in plane geometry.