2018 Theses Doctoral

The Myth of Greek Algebra: Progress and Community in Early-Modern Mathematics

Kaplan, Abram Daniel

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 the relationship between ancient and modern mathematics in order to maintain continuity between their discoveries and the past. In order to do so, I argue, they became increasingly conscious of their professional identity as mathematicians, and they asserted their unique right—over philologists and philosophers—to interpret ancient mathematical texts. Mathematical community with the ancients was purchased at the cost of community with one’s non-mathematical contemporaries.