François Viète
François Viète, known in Latin as Franciscus Vieta, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to his innovative use of letters as parameters in equations. Because of this, Viète is sometimes called "the father of modern algebraic notation". He was a lawyer by trade, and served as a privy councillor to both Henry III and Henry IV of France.
Biography
Early life and education
Viète was born at Fontenay-le-Comte in present-day Vendée. His grandfather was a merchant from La Rochelle. His father, Etienne Viète, was an attorney in Fontenay-le-Comte and a notary in Le Busseau. His mother was the aunt of Barnabé Brisson, a magistrate and the first president of parliament during the ascendancy of the Catholic League of France.Viète went to a Franciscan school and in 1558 studied law at Poitiers, graduating as a Bachelor of Laws in 1559. A year later, he began his career as an attorney in his native town. From the outset, he was entrusted with some major cases, including the settlement of rent in Poitou for the widow of King Francis I of France and looking after the interests of Mary, Queen of Scots.
Serving Parthenay
In 1564, Viète entered the service of Antoinette d'Aubeterre, Lady Soubise, wife of Jean V de Parthenay-Soubise, one of the main Huguenot military leaders, and accompanied him to Lyon to collect documents about his heroic defence of that city against the troops of Jacques of Savoy, 2nd Duke of Nemours just the year before.The same year, at Parc-Soubise, in the commune of Mouchamps in present-day Vendée, Viète became the tutor of Catherine de Parthenay, Soubise's twelve-year-old daughter. He taught her science and mathematics and wrote for her numerous treatises on astronomy and trigonometry, some of which have survived. In these treatises, Viète used decimal numbers and he also noted the elliptic orbit of the planets, forty years before Kepler and twenty years before Giordano Bruno's death.
John V de Parthenay presented him to King Charles IX of France. Viète wrote a genealogy of the Parthenay family and following the death of Jean V de Parthenay-Soubise in 1566 his biography.
In 1568, Antoinette, Lady Soubise, married her daughter Catherine to Baron Charles de Quellenec and Viète went with Lady Soubise to La Rochelle, where he mixed with the highest Calvinist aristocracy, leaders like Coligny and Condé and Queen Jeanne d’Albret of Navarre and her son, Henry of Navarre, the future Henry IV of France.
In 1570, he refused to represent the Soubise ladies in their infamous lawsuit against the Baron De Quellenec, where they claimed the Baron was unable to provide an heir.
First steps in Paris
In 1571, he enrolled as an attorney in Paris, and continued to visit his student Catherine. He regularly lived in Fontenay-le-Comte, where he took on some municipal functions. He began publishing his Universalium inspectionum ad Canonem mathematicum liber singularis and wrote new mathematical research by night or during periods of leisure. He was known to dwell on any one question for up to three days, his elbow on the desk, feeding himself without changing position.In 1572, Viète was in Paris during the St. Bartholomew's Day massacre. That night, Baron De Quellenec was killed after having tried to save Admiral Coligny the previous night. The same year, Viète met Françoise de Rohan, Lady of Garnache, and became her adviser against Jacques, Duke of Nemours.
In 1573, he became a councillor of the Parlement of Rennes, at Rennes, and two years later, he obtained the agreement of Antoinette d'Aubeterre for the marriage of Catherine of Parthenay to Duke René de Rohan, Françoise's brother.
In 1576, Henri, duc de Rohan took him under his special protection, recommending him in 1580 as "maître des requêtes". In 1579, Viète finished the printing of his Universalium inspectionum, published as an appendix to a book of two trigonometric tables. A year later, he was appointed maître des requêtes to the parliament of Paris, committed to serving the king. That same year, his success in the trial between the Duke of Nemours and Françoise de Rohan, to the benefit of the latter, earned him the resentment of the tenacious Catholic League.
Exile in Fontenay
Between 1583 and 1585, the League persuaded king Henry III to release Viète, Viète having been accused of sympathy with the Protestant cause. Henry of Navarre, at Rohan's instigation, addressed two letters to King Henry III of France on March 3 and April 26, 1585, in an attempt to obtain Viète's restoration to his former office, but he failed.Viète retired to Fontenay and Beauvoir-sur-Mer, with François de Rohan. He spent four years devoted to mathematics, writing his New Algebra.
Code-breaker to two kings
In 1589, Henry III took refuge in Blois. He commanded the royal officials to be at Tours before 15 April 1589. Viète was one of the first who came back to Tours. He deciphered the secret letters of the Catholic League and other enemies of the king. Later, he had arguments with the classical scholar Joseph Juste Scaliger. Viète triumphed against him in 1590.After the death of Henry III, Viète became a privy councillor to Henry of Navarre, now Henry IV of France. He was appreciated by the king, who admired his mathematical talents. Viète was given the position of councillor of the parlement at Tours. In 1590, Viète broke the key to a Spanish cipher, consisting of more than 500 characters, and this meant that all dispatches in that language which fell into the hands of the French could be easily read.
Henry IV published a letter from Commander Moreo to the King of Spain. The contents of this letter, read by Viète, revealed that the head of the League in France, Charles, Duke of Mayenne, planned to become king in place of Henry IV. This publication led to the settlement of the Wars of Religion. The King of Spain accused Viète of having used magical powers.
In 1593, Viète published his arguments against Scaliger. Beginning in 1594, he was appointed exclusively deciphering the enemy's secret codes.
Gregorian calendar
In 1582, Pope Gregory XIII published his bull Inter gravissimas and ordered Catholic kings to comply with the change from the Julian calendar, based on the calculations of the Calabrian doctor Aloysius Lilius, aka Luigi Lilio or Luigi Giglio. His work was resumed, after his death, by the scientific adviser to the Pope, Christopher Clavius.Viète accused Clavius, in a series of pamphlets, of introducing corrections and intermediate days in an arbitrary manner, and misunderstanding the meaning of the works of his predecessor, particularly in the calculation of the lunar cycle. Viète gave a new timetable, which Clavius cleverly refuted, after Viète's death, in his Explicatio.
It is said that Viète was wrong. Without doubt, he believed himself to be a kind of "King of Times" as the historian of mathematics, Dhombres, claimed. It is true that Viète held Clavius in low esteem, as evidenced by De Thou:
The Adriaan van Roomen problem
In 1596, Scaliger resumed his attacks from the University of Leyden. Viète replied definitively the following year. In March that same year, Adriaan van Roomen sought the resolution, by any of Europe's top mathematicians, to a polynomial equation of degree 45. King Henri IV received a snub from the Dutch ambassador, who claimed that there was no mathematician in France. He said it was simply because some Dutch mathematician, Adriaan van Roomen, had not asked any Frenchman to solve his problem.Viète came, saw the problem, and, after leaning on a window for a few minutes, solved it. It was the equation between sin and sin. He resolved this at once, and said he was able to give at the same time the solution to the other 22 problems to the ambassador. "Ut legit, ut solvit," he later said. Further, he sent a new problem back to Van Roomen, for resolution by Euclidean tools of the lost answer to the problem first set by Apollonius of Perga. Van Roomen could not overcome that problem without resorting to a trick.
Final years
In 1598, Viète was granted special leave. Henry IV, however, charged him to end the revolt of the Notaries, whom the King had ordered to pay back their fees. Sick and exhausted by work, he left the King's service in December 1602 and received 20,000 écus, which were found at his bedside after his death.A few weeks before his death, he wrote a final thesis on issues of cryptography, which essay made obsolete all encryption methods of the time. He died on 23 February 1603, as De Thou wrote, leaving two daughters, Jeanne, whose mother was Barbe Cottereau, and Suzanne, whose mother was Julienne Leclerc. Jeanne, the eldest, died in 1628, having married Jean Gabriau, a councillor of the parliament of Brittany. Suzanne died in January 1618 in Paris.
The cause of Viète's death is unknown. Alexander Anderson, student of Viète and publisher of his scientific writings, speaks of a "praeceps et immaturum autoris fatum".
Work and thought
New algebra
Background
At the end of the 16th century, mathematics was placed under the dual aegis of Greek geometry and the Arabic procedures for resolution. At the time of Viète, algebra therefore oscillated between arithmetic, which gave the appearance of a list of rules; and geometry, which seemed more rigorous. Meanwhile, Italian mathematicians Luca Pacioli, Scipione del Ferro, Niccolò Fontana Tartaglia, Gerolamo Cardano, Lodovico Ferrari, and especially Raphael Bombelli all developed techniques for solving equations of the third degree, which heralded a new era.On the other hand, from the German school of Coss, the Welsh mathematician Robert Recorde and the Dutchman Simon Stevin brought an early algebraic notation: the use of decimals and exponents. However, complex numbers remained at best a philosophical way of thinking. Descartes, almost a century after their invention, used them as imaginary numbers. Only positive solutions were considered and using geometrical proof was common.
The mathematician's task was in fact twofold. It was necessary to produce algebra in a more geometrical way, and it was also necessary to make geometry more algebraic, allowing for analytical calculation in the plane. Viète and Descartes solved this dual task in a double revolution.