# Francois Vietet: biography, photos and interesting facts

Francois Vietet is a great French mathematician. He initiated algebra as the science of transforming expressions and solving equations in a general form. Wyeth was the first to introduce the letter of both unknowns and given values. He introduced to science the idea that algebraic transformations can be performed not only on values, but also on symbols, and in fact created the concept of a mathematical formula as such. Thanks to this discovery, Viet has made a huge contribution to the creation of alphabetic algebra. Thus, it was he who prepared the ground for the discoveries of Descartes, Fermat and Newton. Today we look at the biography and interesting facts from the life of Francois Vieta.

## Childhood and education

Francois Vietet, whose biography was the subject of our conversation today, was born in 1540 in the town of Ventin-les-Comte, in the south of France. At 60 kilometers from the town is La Rochelle, which at that time was a stronghold of Huguenot Protestants.Despite the fact that for most of his life, Vyet faced the leaders and representatives of this movement, he remained a Catholic. And the reason is not in the protest mood, but in the fact that Viet’s religious peripeteias simply did not care. He was born a Catholic, and did not want to change anything. The father of the future scientist was a prosecutor, and Wyeth, following traditions, followed in his footsteps. He successfully graduated from the University of Poitou and received a law degree.

## Carier start

In 1560, a young lawyer began working in his hometown, but for a long time he did not stay in this position. Three years later, Viet moved into the service of the rich Huguenot family of de Parthenet. In the house of de Parthene, Francois became the secretary of the head of the family and the teacher of his daughter Catherine, who at the time was 12 years old. It was the teaching that prompted interest in mathematics in Mathematics, which he had never noticed before.

When Katerina grew up and found a husband, she moved to Paris. Wyeth did not break up with the Parte de Partenay and also went to the capital. Here it was easier for him to learn about the achievements of the mathematicians known at that time. With some of them, Wyeth even personally met.In particular, he spoke with Professor Sorbonne Ramus and conducted a friendly correspondence with the outstanding Italian mathematician Rafael Bombelli.

## Public service

In 1671, François Viet transferred to the service of the state. At first, he became an adviser to the parliament, and soon an adviser to the French king Henry III.

In 1672, on the night of August 24, there was a large-scale massacre of Huguenots by Catholics, which they called St. Bartholomew at night. That night, Catherine de Parthene's husband and prominent mathematician Ramus died. A few years later, Caterina de Parthene married a second time. She gave her hand and heart to one of the most prominent leaders of the Huguenots - Prince de Rogan. In 1850, at his request, the king of France appointed Wieta to be the reketeer. Thus, Francois received the right on behalf of the king to control the execution of orders throughout the country and to cancel the orders of the major feudal lords.

As a civil servant, Viet did not forget about his predisposition to science. For the first time, he became famous when he was able to decipher the code of the stolen correspondence of the Spanish king with his Dutch representatives.Because of this, Henry the Third knew about the actions of his opponents. The code was complex, and consisted of 600 different characters, which sometimes changed. Having learned that the king of France took possession of the correspondence, the Italians could not believe that someone managed to decipher it. They accused mathematics of having connections with otherworldly forces. To avoid the Inquisition, it was possible only thanks to the authority, which at that time already had Francois Veet. Interesting facts from the life of a scientist are not limited to the history with the code of correspondence. But more about that later.

According to the testimony of contemporaries of Viet, in those days he was very hardworking. Inspired by something, a scientist could work for several days without rest.

## Removal from office

In 1584, the Giza tried to remove Vieta from public service and expelled from Paris. These events have helped the scientist unleash his potential. Having found time to rest and rest, Francois Viett, whose brief biography illustrates his determination, set himself the greatest goal - the creation of a comprehensive mathematics that would allow to solve problems of any level.He was convinced that there was a common, previously unexplored science, which could combine the allegations of the then algebraists and the geometric research of more ancient scholars.

It was during this period that the scientist invented a new alphabetic algebra. The results of his studies were published in 1591, in the treatise "Introduction to the analytical art." In it, the scientist outlined a program of research, which he did not have time to finish before his death. Nevertheless, the main goal was achieved, which followed the Viet Francois. Briefly, it sounds like a transformation of algebra into a more powerful calculus. In his work, the word "algebra" Francois changed to the phrase "analytical art."

In a letter to Catherine de Parthene, François Viet said: “Mathematicians understood that hidden treasures were hidden under algebra, but they could not find them. The tasks that they have positioned as difficult can be easily solved using our art ... ”.

## Species Logistics

So the scientist called the basis of his campaign. Following the example of predecessors, he created a certain system of "species", delimiting the size, number and relationships. For example, this system included: variables, roots, squares, cubes and scalars, which could be used to compare actual dimensions (length, area and volume).For these species, the scientist came up with a special symbolism, denoting each of them with a capital letter of the Latin alphabet.

Francois Vietta was able to illustrate that by working with symbols one can achieve a result applicable to the corresponding quantities, that is, solve problems in a general form. This simple proposition radically changed the development of algebra, opening up the prospect of literal calculus. In order to demonstrate how strong his method is, the scientist in his work provided a stock of formulas that could be used to solve certain problems. The mathematician used the following action signs: plus, minus, root signs and a horizontal line indicating division. The work he denoted by the letter "t". Viet was the first to put brackets into practice. However, in his works they were represented as dashes above the polynomial. In this case, the mathematician did not use many of the characters that were entered before him. For example, he denoted degrees not by numbers, but by the first letters of words or even by whole words.

## Theorem

In 1591, the most famous Vieta theorem was published, which established the connection between the coefficients of a polynomial and its roots.The theorem sounds like this: “If (B + D) A - A2= BD, then A, B, and D are equal. " Today, the French theorem is one of the most famous assertions of the school algebra course. Of course, it is admirable, especially when you consider that it can be generalized to polynomials of any degree.

## Groundwork in geometry

The scientist also achieved serious success in geometry. In this area of knowledge, he was able to develop a lot of interesting methods. In a treatise called “Addition to Geometry,” Wyeth, following the example of the ancients, tried to create something like geometric algebra. Its essence consisted in the use of geometric methods for solving equations of the 3rd and 4th degrees. As the mathematician argued, any equation of these degrees can be solved using the angle trisection method or by building a pair of average proportional.

For centuries, mathematicians were passionate about solving triangles, which were dictated by the needs of architects and astrologers. Viet was able to bring the previously applied methods to a finished form. He was the first to formulate the verbal expression of the cosine theorem. However, equivalent provisions, occasionally met from about the first century BC.The solution of the triangle on two sides and one of the opposing corners, which previously caused difficulties, Vieta received an exhaustive analysis. He clearly said that in this case the solution of the triangle is not always possible. And if there is a solution, then there may be one more, but no more than two.

## Synthesis of algebra and geometry

Thanks to his deep knowledge of algebra, Viet had a huge advantage in his work on geometry. Moreover, his initial interest in algebra was caused by applications to trigonometry, as well as astronomy. It was not for nothing that G. G. Zeiton said: "Trigonometry generously thanked algebra for its assistance." On the one hand, each new application of algebra became the impetus for research in the field of trigonometry. On the other hand, the obtained trigonometric results were a source for new discoveries in the field of algebra. In particular, Vyet derived expressions for sines and cosines of multiple arcs.

## Return to civil service

In 1589, when Heinrich Guise was killed, the king of France ordered mathematics to return to Paris. Soon the king fell at the hands of a monk, who was sent to him by the followers of Giza.Thus, the formal power in the country passed to the head of the Huguenots - Heinrich of Navarre. However, this ruler was recognized by society only in 1593, when he became a Catholic. Thus ended the bloody religious war, which to some extent affected the life of every Frenchman and even those who were completely far from politics and religious upheavals.

Details of the life of mathematics in those days are unknown, as he chose to stay away from the bloody palace intrigues. It is only known that he began to serve the new king. While at court, Francois Wyeth, whose discoveries had already conquered France, served as a government official and was greatly respected by the government as a mathematician.

## Van roomene problem

One day the Netherlands ambassador told King Henry the Fourth that their mathematician van Roomen had presented the task to the society of mathematicians. The ambassador added that in France, apparently, there are no mathematicians, since among those to whom the task was addressed there are no French. The king replied that there was a mathematician in France and called Vieta. The knowledge of cosine and sine of multiple arcs helped the scientist to solve the equation of the 45th degree, which the Dutchman offered him.

## Last years

In the last years of his life, Francois Viett, whose brief biography is coming to an end, left public service, but continued to do science. Once he tried to challenge the introduction of the Gregorian calendar in Europe. He even intended to make his own calendar.

On February 14, 1603, a man of great intelligence and reasoning died. In the memoirs of some French courtiers there was information that the mathematician was married and had a daughter. She became the only heir to the estate of Vieta and 20 thousand ecu, which he left at the head of his bed. That ended his life a great scientist and a very talented man - Francois Viet. Photos in the days of Viet have not done, but the diversity of drawings allows us to get a complete picture of the appearance of the legendary mathematician.

## Application of works

Difficulties in the direct application of the works of Vieta were due to the cumbersomeness of their presentation. Because of this, their full collection has not yet been published. A more or less capacious collection of developments in mathematics was published by the Netherlands scientist baths Scooten in 1646. The book was called "Mathematical Works of Viet." G. G.Ceyton noted that familiarization with the works of Vieta is hampered by the refined form of presentation, and a large number of terms that the scientist invented independently due to his remarkable erudition. Therefore, such a significant influence of a scientist on all subsequent mathematics spread rather slowly.

## Conclusion

Today we met with such an eminent scientist as Francois Viet. Interesting facts from life, summarized in his biography, suggest that the scientist was really a great man. To some extent, he owed his success to Catherine de Porte, whose portrait is presented above. Her connections helped the scientist in the quick realization of his ideas.