Jean Paul de Gua de Malves (1713, Carcassonne – June 2, 1785, Paris) was a French mathematician who published in 1740 a work on analytical geometry in which he applied it, without the aid of differential calculus, to find the tangents, asymptotes, and various singular points of an algebraic curve.
He further showed how singular points and isolated loops were affected by conical projection. He gave the proof of Descartes's rule of signs which is to be found in most modern works. It is not clear whether Descartes ever proved it strictly, and Newton seems to have regarded it as obvious.
De Gua de Malves was acquainted with many of the French philosophes during the last decades of the Ancien Régime. He was an early, short-lived, participant, then editor (later replaced by Diderot) of the project that ended up as the great Encylopédie. Condorcet claimed that it was in fact the Abbé who recruited Diderot to the project, though this claim has never been verified. In either case, Jean-Paul and Jean le Rond d'Alembert, also thought to have been recruited by the Abbé, first show up on the December 1746 payroll of the publishers who were backing the Encylopédie project. Diderot was added just weeks later and took over as editor on 16 October 1747. At the funeral of the "profound geometrician", as Diderot called him, the eulogy was given by Condorcet.
He was elected a Fellow of the Royal Society in 1743.