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Viète, François

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[vyet] (1540–1603) French mathematician: made many early contributions to algebra.

Viète grew up in the Poitou region of France, and in 1556 entered the University of Poitiers to study law. While practising law between 1560 and 1564 he took up cryptography and mathematics as hobbies; the former was useful when he moved to Paris in 1570 and became a court official to Charles IX. The persecution of the Huguenots forced him to go into hiding from 1584, and during this time he absorbed himself in mathematics and did work of historic importance.

After 5 years Henri IV succeeded Charles and Viète returned to the royal court. In the war against Spain, Viète broke the Spanish secret cipher, allowing intercepted dispatches between Philip II of Spain and his embassy to be deciphered. He was dismissed from the court in 1602 and died shortly afterwards.

Viète’s mathematical research was in algebra, which he applied to solve geometrical problems. He used letters to denote constants as well as variables, and he introduced the terms ‘coefficient’ and ‘negative’. Using algebraic methods he solved a problem that dated back to the Greek , that of constructing a circle touching three given circles.

Viète published a systematic account of how to solve problems in plane and spherical trigonometry, making use of all six trigonometric functions for the first time. The cosine law for plane triangles and the law of tangents were included. He also discovered a new and elegant solution to the general cubic equation using trigonometric multiple-angle formulae. The familiar relations between the positive roots of an algebraic equation, its coefficients and the powers of the unknowns are also due to Viète. Always he preferred to establish his identities and his proofs algebraically rather than geometrically, thereby setting a trend.

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