François Viète, the inventor of symbols

History — François Viète, the inventor of symbols

The French jurist and mathematician François Viète (1540–1603), latinised as Vieta, is regarded as one of the fathers of modern algebra. Before him, even the most sophisticated works (such as Cardano’s Ars Magna) wrote equations in an almost narrative form, denoting the unknown with words such as cosa or res. In his In artem analyticen isagoge (1591), Viète had the idea — natural to us today, revolutionary at the time — of denoting by letters both the unknowns (vowels $A,E,I\ldots$) and the known coefficients (consonants $B,C,D\ldots$). This step gave rise to the literal calculus that we use every day: for the first time it was possible to write a general equation and not merely a numerical example.

The formulae that today bear his name — the sum and product of the solutions of a polynomial expressed in terms of the coefficients — were discovered by Viète while studying equations of arbitrary degree. Curiously, Viète himself did not accept negative numbers, and his formulae remained valid only for positive solutions: the modern generalisation came later (Boyer, ch. 12).

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Topics: Quadratic equations
Concepts: Literal calculus · Sum and product of roots
People: Gerolamo Cardano · François Viète (Vieta)