The Myth of Greek Algebra

Abram Daniel Kaplan

This dissertation traces the reception of Greek mathematics by practicing mathematicians in England and France, ca. 1580-1680. The period begins with the newly widespread availability of works by Pappus, Apollonius, and Diophantus; it concludes with the invention of calculus by Isaac Newton and Gottfried Leibniz. The dissertation focuses on a philological imaginary created by François Viète (fl. 1580-1600) that I call “the myth of Greek algebra”: the belief that the ancient Greek geometers concealed their heuristic method and only presented their results. This belief helped mathematicians accommodate ancient Greek works to their own mathematical ends; it helped mathematicians sustain the relevance of Greek texts for their own inventions. My study focuses on Viète, Rene Descartes, John Wallis, Isaac Newton, and Gottfried Leibniz: I show how these mathematicians continually renovated...