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François Viète - Life
François Viète (or Vieta, as he is often known by his latinized name) was born in 1540 in Fontenay-le-Comte, France. Educated in a cloister school, then at the University of Poitiers, he took up the practice of law in his home town. He soon rose to prominence by his astute legal services to prominent people, and later served as royal councilor to Kings Henry III and Henry IV of France. In his spare time he worked on mathematics and published his results at his own expense. He has been called the father of modern algebra [Enc. Brit.] and the foremost mathematician of the sixteenth century [Kline, p. 239].
A few stories will indicate something of his character. While working for King Henry III, he discovered the key to a Spanish cipher of 500 characters, and so was able to read the secret correspondence of his enemies. Philipp II of Spain was so sure that his code was invulnerable that when he heard of this, he complained to the Pope that the French were using sorcery against him, contrary to good Christian morals. [Enc. Brit.].
Viète's tact in dealing with people is illustrated by the case of Françoise de Rohan, a cousin of Henry III. She had been engaged to the duke J. de Nemours, and had a son by him, but then he married another woman, Anne d'Este. Françoise wanted him declared her legal husband, and his children by Anne declared bastards. Viète found a solution in that parliament declared her the legal wife of Nemours, and gave her a property as her dukedom, but they also declared the marriage dissolved, so that Anne d'Este and her children were not harmed either in honor or property. [Opera, 1970, Vorwort].
Viète's mathematical skill appears in the following incident from the summer of 1594. The Belgian mathematician A. van Roomen had proposed a challenge to all contemporary mathematicians, to solve a certain equation of the 45th degree. The Dutch ambassador presented van Roomen's book to King Henry IV with the comment that apparently there were no mathematicians of any importance in France. The King called for Viète who immediately found one solution to the equation, and then next day presented 22 more. [Opera, 1970, Vorwort].
In response to van Roomen, Viète challenged him to solve the problem of Apollonius, to construct a circle tangent to three given circles. When Adrianus Romanus wanted to effect a solution using two hyperbolas, Viète was little content with that solution, because it was alien to the usage of geometers, according to which in the solution of problems that are called plane, only circles and lines should be used. He himself gave a universal solution to that problem of tangencies by a more geometric method, and published a little book in 1600 in Paris, to which he gave the title Apollonius Gallus [Opera, pp 325-346]. Adrianus was so pleased with this work that he immediately set out for France to see Viète, and struck up an intimate friendship with him. Viète received him hospitably, was together with him for a whole month, and took care of him to the extent of his resources. [Camerer, introduction].
We may be surprised that such a busy lawyer as Viète should have had any time for mathematics. But he had a contemplative life as well. A contemporary historian said in 1620, his meditations were so profound that he was often seen fixed in cogitation for three days continuously, sitting at his eating table without food or sleep, except what he could get leaning on his elbow, and neither moved nor sought refreshment at natural intervals .[Vita prefixed to Opera]
Viète died in 1603, less than three months after he had received the King's permission to retire from public life.