François Viète

François Viète or Franciscus Vieta, as he called himself in Latinized form (* 1540 in Fontenay -le- Comte, † December 13, according to other sources February 23, 1603 in Paris ) was a French lawyer and mathematician. He introduced the use of letters as variables in mathematical notation of modern times.

Life

François Viète was born the son of the respected lawyer Étienne Viète 1540 in Fontenay -le- Comte ( in the present province of Vendée in Western France). He came from a wealthy middle-class family. Viète attended a convent school and began to study with the intention of pursuing a university career with 18 years of jurisprudence in Poitiers.

After completing his studies he settled in his native city as a lawyer. First ( 1564), he accepted a position as secretary and legal adviser to the very influential and wealthy Protestant family Soubise. In addition, he taught as a private tutor, the daughter of the family, Catherine Parthenay, is likely to have influenced him their interest in astronomy, astrology and mathematics. In this way, a work of Viète on the representation theory of the planets on the basis of the Ptolemaic geocentric system was created.

From 1570 he worked as a lawyer in Paris and soon enjoyed an excellent reputation. After the death of his father he inherited the title of Sieur de la Bigotière. 1574 he was appointed a Member of Parliament in Rennes. From 1580 lived Viète again in Paris, also worked there in Parliament and as a personal adviser to the king. He served as a counselor of kings Henry III. (1551-1589) and Henry IV (1553-1610), for which he deciphered among other intercepted messages of war opponent Spain. He signed as " interprète déchiffreur et du roi ".

Due to political intrigue - especially through the influence of the Catholic League and the Guise family - he was released in 1584 and retired to the country where he mainly dealt with mathematics. After the assassination of Henry III. he was appointed in 1589 but of his successor Henry IV returned to his former position.

Around this time he gained an international reputation as a mathematician. The anecdote is known of his meeting with Adriaan van Roomen ( Adrianus Romanus, 1561-1615 ), which is told in numerous sources, including the " Historiettes " of Tallemant of Réaux. Van Roomen was a native of lions mathematician who was then teaching in Würzburg. He had found a job as a challenge to all mathematicians of Europe and was of Viete solution so excited that he left immediately to France to meet with him. Viète, the dry, the rapidity of its solution later with legitimate Ut, ut solvi ( read How so released) commented, put his hand van Roomen the task of finding all circles which touch three given circles (Apollo African problem). This problem had already been solved in antiquity by Apollonius of Perga, the writing of Apollonius got lost. Van Roomen solved the problem with the help of a hyperbola. This solution was maintained by Viète for inadequate because it is not limited to the classical method with ruler and compass. Viète published later himself an improved solution in his Apollonius Gallus.

Since it went Viète health getting worse, he asked the king for his release in 1602, to recover. But he never recovered and died on December 13, 1603 in Paris.

Viète lived in a time that was marked by bitter religious struggles between the Catholics and the Protestant Huguenots. He was indeed a Catholic, as well as the king, but also wrong in Protestant circles and was the " politiques " near who sought to overcome the religious antagonisms and national unity in contrast to the Catholic League.

Merits as a mathematician

Actually, the math was just a sideline for Viète, yet he became one of the most important and influential mathematicians of his time.

He is sometimes called the "father of algebra ", as he introduced the computation with letters in modern times and systematically symbols for arithmetic operations used, especially as he realized that this opened up many more possibilities than before. Already in ancient mathematics, however, Diophantus of Alexandria had used a letter symbolism. Viète eventually led calculating with ( great Latin ) letters, which is based on the same principles as calculating with numbers. He distinguished the " Logistica numerosa " as a pure numerical calculation of the more abstract " Logistica speciosa ", the " letters Computing" and can thus be referred to as the founder of modern algebra. Our present spelling is largely due to him. He used first consistently (with few exceptions) symbols for mathematical operations and reduced whole mathematical formulas complexes.

• So he used the sign first used by Johannes Widmann in a book in 1489 and - in his works. Previously, this had been advertised in arithmetic operations usually as plus and minus
• He also used the fraction bar as a symbol of the division and the word "in" as a fixed abbreviation of multiplication.
• The equality of two terms Viète expressed by the word " aequabitur " and thus invented the first equal sign. Belong together Terme Vieta wrote to each other and combined them with braces.

In addition, he has made outstanding results in the field of trigonometry and made ​​valuable groundwork for the subsequent development of the calculus. In this context, he described in 1593 as first a closed formula for the circle constant π in the form of an infinite product ( see main article Vieta's product representation of the circle number ).

Today it is known, the set of Vieta on the solutions of a quadratic equation.

The asteroid ( 31823 ) Viète and the moon crater Vieta were named after him.

Works

Viète has published numerous works that are, however, mostly appeared only in small numbers and were intended for his friends. The first complete edition after his death in 1646 by Frans van Schooten in Leiden by Elsevier under the title Opera mathematica, in unum volume congesta, ac recognita, opera atque studio Francisci Schooten published (reprinted Hildesheim: Olms 1970). His major works include:

• Canon mathematicus seu ad triangula ( 1579)
• Liber singularis ( 1579)
• Isagoge in artem analyticam ( 1591 )
• Apollonius Gallus (1600)
• Relatio Kalendarii vere Gregorian (1600)
• Apud Christophorum clavium expostulatio (1602 )

Newer editions:

• Karin Reich, Helmuth Gericke Francois Viète: Introduction to the New Algebra, Historiae scientiarum elementary, Volume 5, Munich: Fritsch, 1973 ( translation of Isagoge 1591 )