Viète's new algebra | Tangente

In the 9^th century, al-Khwarizmi wrote a text on solving equations that may be regarded as the first treatise on algebra. His name, altered and reinterpreted, gave rise to the word "algorithm", while al-jabr, one of his techniques for solving equations, gave rise to the word "algebra". His writings contain no letters or symbols, yet they are nonetheless "algebra". The procedures are justified by geometric proofs. The giant leap from rhetorical to symbolic algebra still remained to be made. François Viète made that leap possible and paved the way for his successors, including René Descartes (1596–1650). In 1630, to promote this invention, the Sieur de Vaulezard would translate Viète's major work in the field from Latin, In Artem Analyticem Isagoge ("Introduction to the Analytic Art"), and publish it under the title The New Algebra of Mr Viète.

Viète's double life --------------------

François Viète was born in 1540, either in Fontenay-le-Comte or in Foussais-Payré, in the Vendée. He studied at the Franciscan Collège des Cordeliers, which Rabelais had also attended. His legal studies led to a career as a lawyer. His exceptional abilities attracted attention, and he became an adviser to the Soubise family and tutor to Catherine de Parthenay, who would play an important role in his mathematical work. He served as a councillor in the Parlement of Brittany, then as master of requests and adviser to King Henry III during a highly turbulent period—he was in Paris during the St Bartholomew's Day massacre. Suspended from this post from 1584 to 1589, he prudently took refuge in Beauvoir-sur-Mer. These five years allowed him to devote himself to his favourite pastime, mathematics, for which his official duties had left him little time. It was there, in particular, that he wrote his major work. In 1589, he resumed his duties as adviser to King Henry IV. Exhausted and ill, he died in Paris in 1603.

"He pondered with such diligence that he was often seen to remain in his study for three whole days without eating, and even without sleeping except when, from time to time, he rested his head on his hand to restore his strength with a few moments of sleep. […] He died young, for he worked himself to death." (Jacques Auguste de Thou (1553–1617), Éloge de Viète, in Histoire universelle, volume 14)