The foundations of differential calculus: the 1700 quarrel | Tangente

1700: debates between Rolle and Varignon at the Academy --------------------------------------------------

Jean Bernoulli was chiefly responsible for popularizing in France a "new method" of calculus created by Leibniz in 1684, giving paid lessons to his patron, the Marquis Guillaume de L'Hospital (1661–1704), who published the first treatise on differential calculus in 1696. But in February 1697, Philippe de La Hire (1640–1718) presented a short memoir to the Royal Academy of Sciences, in which he expressed reservations about the method of infinitesimals, which, if not handled carefully, can lead to errors.

His doubts were shared by Abbé Bignon (president of the Academy sixteen times between 1699 and 1734!) and Michel Rolle, who opened a debate on 17 July 1700 with a memoir attacking the lack of rigor in the fundamental concepts of Leibnizian calculus. Pierre Varignon then, reluctantly, took up the defense of the new calculus in August 1700: "The Marquis de L'Hospital is still in the country, so that I find myself alone here entrusted with the defense of the infinitesimals, of which I am the true martyr, having already withstood so many assaults on their behalf against certain mathematicians of the old school, who, vexed to see young people catch up with them through this calculus and even surpass them, do everything they can to discredit it, though we cannot get them to put anything in writing against it."