François Viète (also known as Franciscus Vieta) Biography

Many scholars consider François Viète the seminal algebraist of the 16th century. Although he worked in mathematics in his spare time and was regarded as an amateur mathematician, he has contributed numerous improvements, solutions, and other vital developments to mathematics. For example, Viète had a hand in the development of modern algebra by devising algebraic notation, using letters to denote quantities, both unknown and known. He also contributed to the theory of equations, and introduced algebraic terms, such as "coefficient," that are still used today. Among Viète's other significant mathematical accomplishments are: using algebra to solve longstanding geometrical problems; calculating to 10 places, an important accomplishment of his time; playing a role in the improvements brought by the development of Julian calendars; and having a public hand in the mathematical controversies of his era.

Viète was born in Fontenay-le-Comte, Poitou, France, to Étienne (a lawyer and notary) and his wife, Marguerite Dupont. After receiving his education in Fontenay--partly from monks at a local Franciscan cloister--he studied law at the university in Poiters beginning in 1556. Upon graduation with a bachelor's degree, he worked as a lawyer in Fontenay for four years. Viète was apparently successful in this career; he counted among his clients Queen Eleanor of Austria and Mary Stuart. During this period, Viète also began conducting mathematical research on the side, as well as cosmological and astronomical studies.

In 1564, Viète became closely involved with the aristocratic Soubise family, including Antoinette d'Aubeterre, who consulted him on legal matters. Viète stopped practicing law to serve as private secretary to d'Aubeterre. He moved with the family to La Rochelle where he tutored d'Aubeterre's daughter, Catherine de Parthenay, until her marriage in 1570. During this time, Viète decided to become a Huguenot (French Protestant). These years also mark the first period where Viète had a significant amount of time to devote to his mathematical research.

After his charge's marriage, Viète's primary occupation became service in the royal courts. He was appointed by King Charles IX to serve as a councilor to Brittany's parliament at Rennes in 1573, a post he held until 1580. He then served Charles IX and his successor, Henry III, in Paris as member of the privy counsel and the maître de requêtes (Master of Requests). In 1584, soon after Henry III came to the throne, Viète was forced from the royal court because of his Huguenot sympathies. He spent the next five years in cities such as Garnache, Fontenay, and Bigotière, where he devoted his full attention to mathematics and related research. This marks Viète's second fruitful period of mathematical work.

Viète's ties to the royal court allowed his work to be printed by the royal printer, Jean Mettayer, who published most of Viète's mathematical treatises. Viète's first important book, Canon mathematicus seu ad triangula cum appendibus("Mathematical Laws Applied to Triangles") was published in 1579. One of Viète's goals as a mathematician was to give more credence to trigonometryin the mathematical world and this text contributed significantly to this cause. Using all six trigonomic functions, he solved problems on plane and spherical triangles.

In 1589, Viète was invited to the court of Henry III (then in Tours) as a counselor to the French parliament. In the same year, he was appointed a royal Privy Councilor, and broke the code used by Philip II of Spain for internal messages when France was at war with Spain in 1589-90. Henry IV ascended to the French throne in 1589 upon Henry III's death, and, like his royal patron, Viète declared himself Catholic. He stayed in service at the court--following it to Paris in 1594--and remained there until his retirement in 1602.

These years also saw Viète publishing a series of important works. The most influential of these was his 1591 In artem analyticam Isagoge("Introduction to the Analytical Arts"), an algebra text. In this work he introduced the first systematic use of symbolic algebraic notation. Viète demonstrated, for example, the value of symbols by using the plus and minus signs for operations, vowels for unknown quantities (variables), and consonants for known quantities (parameters). He also delineated new ways of solving cubic equations, using, among other approaches, trigonometry. This book helped algebra develop further, and is perhaps one of the earliest identifiable "modern" algebra textbooks.

Two years later, in 1593, Supplementum geometriaewas published. Although published in 1593, Viète had probably written this treatise in 1591. Among the many geometric topics in this and a second volume published the same year were solutions to the problem of the trisection of an angle and the corresponding cubic equation, the doubling of the cube, the construction of the regular heptagon inscribed in a circle, and the earliest known explicit expression for as an infinite product. The last significant work of Viète's published in his lifetime was De numerosa potestatum puarum atque ad fectarum ad exegesin resolution e tractatcus (1600). In it, he delineates a way of approximating roots of numerical equations. He also solved the fourth Apollonian problem, which concerns three circles and the construction of a fourth tangent to the other three.

Twelve years after his death, De aquationem recognitione et emedatione libri duo("Concerning the Recognition and Emendation of Equations ") was published. It was Viète's primary text dealing with the theory of equations; he developed methodology for solutions of second, third, and fourth degree equations. Viète also introduced the term "coefficient" in this treatise.

Viète died December 13, 1603 (or February 23, 1603, depending on the source) in Paris, France. It is known that he was twice married, first to Barbe Cotherau and later, after becoming a widower, to Juliette Leclerc. He had at least one child, but details concerning his marriages and children are sketchy.