**François Viète** was a French amateur mathematician and astronomer who introduced the first systematic algebraic notation in his book *In artem analyticam isagoge *. He was also involved in deciphering codes.

- After graduating with a law degree in 1560, Viète entered the legal profession but he only continued on this path for four years before deciding to change his career.
- In 1564 Viète took a position in the service of Antoinette d'Aubeterre.
- In 1570 Viète left La Rochelle and moved to Paris.
- Although he was never employed as a professional scientist or mathematician, Viète was already working on topics in mathematics and astronomy and his first published mathematical work appeared in Paris in 1571.
- While Viète was in Paris, Charles IX authorised the massacre of the Huguenots, who were an increasingly powerful group of French Protestants, on 23 August 1572.
- This must have been an extremely difficult time for Viète for, although not active in the Protestant cause, he was a Huguenot himself.
- However, on 24 October 1573 Charles appointed Viète to the government of Brittany which was based at Rennes.
- Viète moved to Rennes to take up his position of counsellor there.
- Leaving Paris, Viète went to Beauvoir-sur-Mer, on the coast about 130 km northwest of his home town of Fontenay-le-Comte.
- During the five years that he spent at Beauvoir-sur-Mer, Viète was able to devote himself entirely to his mathematical studies.
- In many ways Viète's enemies did mathematics a favour, for it was during this period without formal duties that Viète's most important mathematics was done.
- It took Viète some time to crack the complicated code.
- At first he was only able to decode parts of the message and forwarded parts to Henry IV, but eventually Viète sent him the fully decoded message on 15 March 1590.
- Although Viète was never a professional mathematician, he did lecture on mathematics.
- Viète followed the example of his king and also converted to Roman Catholicism.
- During the period referred to in the previous paragraph, Viète had again come to the King's rescue by solving a mathematical problem.
- Henry put the problem to Viète who solved it by realising that there was an underlying trigonometric relation.
- As a result of this a friendship grew up between Viète and Roomen.
- Viète proposed the problem of drawing a circle to touch 3 given circles to Roomen (the Apollonian Problem) and Roomen solved it using hyperbolas, publishing the result in 1596.
- Viète continued to serve Henry IV in Paris until 1597 when he went back to his home town of Fontenay-le-Comte.
- Some of Viète's first work was directed towards the production of a major work on mathematical astronomy Ad harmonicon coeleste.
- Perhaps rather surprisingly Viète came to the conclusion that Copernicus's theory was not valid geometrically.
- Although the Ad harmonicon coeleste was never published, Viète did begin publishing the Canon Mathematicus in 1571 which was intended as a mathematical introduction to the astronomy treatise.
- Viète introduced the first systematic algebraic notation in his book In artem analyticam isagoge published at Tours in 1591.
- However, Viète did not find Arabic mathematics to his liking and based his work on the Italian mathematicians such as Cardan, and the work of ancient Greek mathematicians.
- One would have to say, however, that had Viète had a better understanding of Arabic mathematics he might have discovered that many of the ideas he produced were already known to earlier Arabic mathematicians.
- In his treatise In artem analyticam isagoge Viète demonstrated the value of symbols introducing letters to represent unknowns.
- Perhaps it is worth noting that the word "coefficient" is actually due to Viète.
- When Viète applied numerical methods to solve equations as he did in De numerosa potestatum he gave methods which were similar to those given by earlier Arabic mathematicians.
- He deduces that the work of Viète is not based on that of Sharaf al-Din al-Tusi.
- Viète also wrote books on trigonometry and geometry such as Supplementum geometriae (1593).
- In 1593 Viète published a second book, which in many ways was motivated by his lecture course at Tours in the previous year (which we mentioned above), examining various problems such as doubling the cube, trisecting an angle and the construction the tangent at any point on an Archimedian spiral.
- On the other hand it is unfair to Viète since his contributions were of much wider mathematical importance.
- It would also be interesting to know how much Viète's ideas were influenced by those of Harriot.
- it appears that Harriot's system of analytics or algebra was based on that of his friend and correspondent François Viète as Viète's was avowedly based on that of the ancients.
- Although this seems to make Harriot's dependence on Viète clear, one would have to say that the two men give very similar approaches to solving equations algebraically, yet Harriot shows deeper understanding than does Viète.

Born 1540, Fontenay-le-Comte, Poitou (now Vendée), France. Died 13 December 1603, Paris, France.

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Algebra, Analysis, Astronomy, Geometry, Number Theory, Special Numbers And Numerals

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive