Viète

François Viète, Latinized as Franciscus Vieta, was a French mathematician born around 1540 in Fontenay-le-Comte and who died in 1603 in Paris. He is regarded as a foundational figure in the development of modern algebra for introducing symbolic notation and a systematic approach to solving equations.

Viète is best known for his pioneering use of letters to denote unknown quantities and coefficients in algebra. In his treatise In artem analyticem isagoge (published in 1591), he proposed using symbols such as x, y, and z for unknowns, and a, b, c for coefficients, thereby transforming algebra into a general, rule-based discipline rather than a collection of numerical recipes. This notation laid the groundwork for later developments in algebra and influenced the way problems were formulated and solved.

Another central contribution is associated with what are now called Vieta’s formulas. Viète studied the relationships between the roots of polynomial equations and the coefficients of those polynomials, showing how sums and products of the roots can be expressed in terms of the coefficients. These ideas established a structural link between the roots and the equation itself, influencing subsequent advances in algebra and analytic geometry, including the work of Descartes.

Viète’s advocacy of symbolic notation helped shift mathematics from rhetorical and numerical descriptions to general, abstract reasoning. His innovations facilitated the generalization of problem-solving techniques and are recognized as a turning point in the history of algebra.