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BIOGRAPHIES OF GREAT SCIENTISTS
Viet François. Biography of a scientist
Directory / Biographies of great scientists
François Viet is a remarkable French mathematician who laid the foundation for algebra as a science of transforming expressions, of solving equations in a general form, the creator of literal calculus. Viet was the first to designate by letters not only unknowns, but also given quantities. Thus, he managed to introduce into science the great idea of the possibility of performing algebraic transformations on symbols, that is, to introduce the concept of a mathematical formula. In this way, he made a decisive contribution to the creation of literal algebra, which completed the development of Renaissance mathematics and paved the way for the appearance of the results of Fermat, Descartes, and Newton. Francois Viet was born in 1540 in the south of France in the small town of Fantenay-le-Comte, which is located 60 km from La Rochelle, which at that time was a stronghold of French Huguenot Protestants. Most of his life he lived next to the most prominent leaders of this movement, although he himself remained a Catholic. Apparently, religious differences did not bother the scientist. Vieta's father was a prosecutor. According to tradition, the son chose his father's profession and became a lawyer after graduating from the University of Poitou. In 1560, the twenty-year-old lawyer began his career in his native city, but three years later he moved to the service of the noble Huguenot de Partenay family. He became the secretary of the master of the house and the teacher of his twelve-year-old daughter Ekaterina. It was teaching that aroused in the young lawyer an interest in mathematics. When the student grew up and got married, Viet did not part with her family and moved with her to Paris, where it was easier for him to learn about the achievements of the leading mathematicians of Europe. With some scientists Viet met personally. So, he communicated with the prominent professor of the Sorbonne Ramus, with the largest mathematician in Italy, Rafael Bombelli, carried on friendly correspondence. In 1571, Viète moved into the civil service, becoming an advisor to Parliament and then an advisor to King Henry III of France. On the night of August 24, 1572, a massacre of the Huguenots by Catholics took place in Paris, the so-called St. Bartholomew's Night. That night, along with many Huguenots, the husband of Catherine de Parthenay and the mathematician Ramus perished. A civil war broke out in France. A few years later, Catherine de Parthenay remarried. This time, one of the prominent leaders of the Huguenots, Prince de Rogan, became her chosen one. At his request, in 1580, Henry III appointed Vieta to the important state post of reketmeister, which gave the right to control the execution of orders in the country on behalf of the king and suspend the orders of large feudal lords. While in public service, Viet remained a scientist. He became famous for being able to decipher the intercepted correspondence of the King of Spain with his representatives in the Netherlands, thanks to which the King of France was fully aware of the actions of his opponents. The code was complex, containing up to 600 different characters, which changed periodically. The Spaniards could not believe that they had deciphered it, and accused the French king of having links with evil spirits. The evidence of Vieta's contemporaries about his enormous ability to work dates back to this time. Being passionate about something, the scientist could work for three days without sleep. In 1584, at the insistence of the Guises, Vieta was removed from office and expelled from Paris. It was during this period that the peak of his work falls. Having found unexpected peace and rest, the scientist set as his goal the creation of a comprehensive mathematics that would allow solving any problems. He developed the conviction that "there must be a general, still unknown science, embracing both the witty inventions of the latest algebraists and the deep geometric researches of the ancients." Vieta outlined the program of his research and listed treatises, united by a common idea and written in the mathematical language of the new alphabetic algebra, in the famous "Introduction to Analytical Art" published in 1591. The enumeration went in the order in which these works were to be published in order to form a single whole - a new direction in science. Unfortunately, a single whole did not work out. The treatises were published in a completely random order, and many saw the light only after Vieta's death. One of the treatises was not found at all. However, the main idea of the scientist was remarkably successful: the transformation of algebra into a powerful mathematical calculus began. The very name "algebra" Vieta in his writings replaced the words "analytical art". He wrote in a letter to de Partenay: "All mathematicians knew that under algebra and almukabala ... incomparable treasures were hidden, but they did not know how to find them. The tasks that they considered the most difficult are quite easily solved by dozens with the help of our art ..." Viet called the basis of his approach species logistics. Following the example of the ancients, he clearly distinguished between numbers, magnitudes and relations, collecting them into a certain system of "species". This system included, for example, variables, their roots, squares, cubes, square-squares, etc., as well as many scalars, which corresponded to real dimensions - length, area or volume. For these species, Viet gave special symbols, designating them in capital letters of the Latin alphabet. Vowels were used for unknown quantities, consonants were used for variables. Viet showed that, by operating with symbols, it is possible to obtain a result that is applicable to any relevant quantities, that is, to solve the problem in a general form. This marked the beginning of a radical change in the development of algebra: literal calculus became possible. Demonstrating the power of his method, the scientist brought in his works a stock of formulas that could be used to solve specific problems. Of the action signs, he used "+" and "-", the radical sign and the horizontal bar for division. The work was denoted by the word "in". Viet was the first to use brackets, which, however, he did not have the form of brackets, but lines over a polynomial. But he did not use many of the signs introduced before him. So, a square, a cube, etc. denoted by words or the first letters of words. The famous theorem establishing the connection between the coefficients of a polynomial and its roots was published in 1591. Now it bears the name of Vieta, and the author himself formulated it as follows: "If B + D times A minus A squared equals BD, then A equals B and equals D." Vieta's theorem has now become the most famous statement in school algebra. Vieta's theorem is admirable, especially since it can be generalized to polynomials of any degree. The scientist also achieved great success in the field of geometry. With regard to it, he managed to develop interesting methods. In the treatise "Additions to Geometry", he sought to create, following the example of the ancients, some kind of geometric algebra, using geometric methods to solve equations of the third and fourth degrees. Any equation of the third and fourth degree, Viet argued, can be solved by the geometric method of trisecting an angle or by constructing two mean proportionals. For centuries, mathematicians have been interested in the question of solving triangles, as it was dictated by the needs of astronomy, architecture, and geodesy. With Vieta, the previously used methods for solving triangles acquired a more complete form. Thus, he was the first to explicitly formulate the cosine theorem in verbal form, although provisions equivalent to it were sporadically applied from the first century BC. Previously known for its difficulty, the case of solving a triangle given two given sides and one of the angles opposite them received an exhaustive analysis by Vista. It was clearly stated that in this case a solution is not always possible. If there is a solution, then there may be one or two. A deep knowledge of algebra gave Vieta great advantages. Moreover, his interest in algebra was initially caused by applications to trigonometry and astronomy. "And trigonometry, - as G. G. Zeiten notes, - generously thanked algebra for the help it provided." Not only did each new application of algebra give impetus to new research in trigonometry, but the trigonometric results obtained were the source of important advances in algebra. Vieta, in particular, belongs to the derivation of expressions for the sines (or chords) and cosines of multiple arcs. In 1589, after the assassination of Henry of Guise by order of the king, Viet returned to Paris. But in the same year, Henry III was killed by a monk - an adherent of Guise. Formally, the French crown passed to Henry of Navarre, the head of the Huguenots. But only after this ruler converted to Catholicism in 1593, in Paris he was recognized as King Henry IV. Thus was put an end to the bloody and destructive religious war, which for a long time influenced the life of every Frenchman, even who was not at all interested in politics or religion. The details of Vieta's life during that period are unknown, which in itself speaks of his desire to stay away from the bloody palace events. It is only known that he went to the service of Henry IV, was at court, was a responsible government official and enjoyed great respect as a mathematician. According to legend, the ambassador of the Netherlands said at a reception with King Henry IV of France that their mathematician van Roomen had given the mathematicians of the world a problem. But in France, apparently, there are no mathematicians, since among those to whom the challenge was especially addressed, there is not a single Frenchman. Henry IV replied that there was a mathematician in France and invited Vieta. Knowledge of the sines and cosines of multiple arcs enabled Viet to solve the 45th degree equation proposed by the Dutch scientist. In the last years of his life, Viet retired from public service, but continued to be interested in science. It is known, for example, that he entered into controversy over the introduction of a new, Gregorian calendar in Europe. I even wanted to create my own calendar. In the memoirs of some French courtiers, there is an indication that Viet was married, that he had a daughter, the only heiress of the estate, by which Viet was called seigneur de la Bigault. In the court news, the Marquis Letual wrote: "... On February 14, 1603, Mr. Viet, rocket master, a man of great intelligence and reasoning and one of the most learned mathematicians of the century, died ... in Paris, having, by all accounts, 20 thousand ecu at the head. He was over sixty years old. Direct application of the works of Vieta was very difficult due to the heavy and cumbersome presentation. Because of this, they have not been fully published so far. A more or less complete collection of Vieta's works was published in 1646 in Leiden by the Dutch mathematician van Skooten under the title Vieta's Mathematical Works. G. G. Zeiten noted that “reading Vieta’s works is hampered by a somewhat refined form in which his great erudition shows through, and a large number of Greek terms invented by him and completely unaccustomed. Therefore, his influence, so significant in relation to all subsequent mathematics, spread relatively slowly. Author: Samin D.K.
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