Viète, who was born at Fontenay-le-Comte in France, is also known by the Latinized form of his name, Franciscus Vieta. He was educated at Poitiers where he studied law and for a time he practiced as a lawyer. He was a member of the parlement of Brittany but because of his Huguenot sympathies he was forced to flee during the persecution of the Huguenots. On Henry IV's accession, however, he was able to hold further offices and became a privy councillor to the king. He put his mathematical abilities to practical use in deciphering the code used by Spanish diplomats.

Viète's chief work was in algebra. He made a number of innovations in the use of symbolism and several technical terms still in use (e.g., coefficient) were introduced by him. His work is important because of his tendency to solve problems by algebraic rather than geometric methods. By bringing algebraic techniques to bear on them Viète was able to solve a number of geometrical problems. A particularly longstanding problem – formulated by the Greek geometer Apollonius of Perga – namely, how to construct a circle that touches three given circles, was solved in this way by Viète.

Viète's major work is contained in his treatise In artem analyticem isagoge (1591; Introduction to the Analytical Arts) and among other advances in algebra that it contains are new and improved methods for solving cubic equations. Among these are techniques that make use of trigonometric methods. Viète also developed methods of approximating the solutions to equations.