Hudde studied law at the
University of Leiden, but turned to mathematics under the influence of his teacher
Frans van Schooten. From 1654 to 1663 he worked under van Schooten.
La Géométrie (1637) by
René Descartes provided an introduction to
analytic geometry in French, whereas
Latin was still the international language of science. Schooten and his students including Hudde,
Johan de Witt and
Hendrik van Heuraet published a Latin translation of
La Geometrie in 1659. Each of the students added to the work. Hudde's contribution described
Hudde's rules and made a study of
maxima and minima. He added to the translation of
La Geometrie two papers of his own:
Epistola Prima de Reductione Aequationum on algebraic equations, and
Epistola Secunda de Maximis et Minimis, in which he described an algorithm for simplifying the calculations necessary to determine a double root to a polynomial equation. Together with
René-François de Sluse, Hudde provided general algorithms by which one could routinely construct tangents to curves given by
polynomial equations. Hudde corresponded with
Baruch Spinoza and
Christiaan Huygens,
Johann Bernoulli,
Isaac Newton and
Leibniz. Newton and Leibniz mention Hudde, and especially Hudde's rule, many times and used some of his ideas in their own work on
infinitesimal calculus. ==See also==