Michel Rolle (April 21, 1652 – November 8, 1719) was a French mathematician. He is best known for Rolle's theorem (1691), and he deserves to be known as the co-inventor in Europe of Gaussian elimination (1690).
Rolle was born in Ambert, Basse-Auvergne. He moved from Ambert to Paris in 1675, and he was admitted to the Académie Royale des Sciences in 1685. Rolle was promoted to a salaried position in the Academy, a pensionnaire géometre, in 1699. This was a distinguished post because of the 70 members of the Academy, only 20 were paid. He had then already been given a pension by Jean-Baptiste Colbert after he solved one of Jacques Ozanam's problems. Rolle died in Paris. No portrait of him is known.
In 1690, Rolle published Traité d'Algebre. It contains the first published description in Europe of the Gaussian elimination algorithm, which Rolle called the method of substitution. Some examples of the method had previously appeared in algebra books, and Isaac Newton had previously described the method in his lecture notes, but Newton's lesson was not published until 1707. Rolle's statement of the method seems not to have been noticed in so far as the lesson for Gaussian elimination that was taught in 18 and 19th century algebra textbooks owes more to Newton than to Rolle.
Rolle is best known for Rolle's theorem in differential calculus. Rolle had used the result in 1690, and he proved it (by the standards of the time) in 1691. Given his animosity to infinitesimals it is fitting that the result was couched in terms of algebra rather than analysis. Only in the 18th century was the theorem interpreted as a fundamental result in differential calculus. Indeed, it is needed to prove both the mean value theorem and the existence of Taylor series. As the importance of the theorem grew, so did the interest in identifying the origin, and it was finally named Rolle's theorem in the 19th century. Barrow-Green remarks that the theorem might well have been named for someone else had not a few copies of Rolle's 1691 publication survived.
Critique of infinitesimal calculus 
In a criticism of infinitesimal calculus that predated George Berkeley's, Rolle presented a series of papers at the French academy, alleging that the use of the methods of infinitesimal calculus leads to errors. Specifically, he presented an explicit algebraic curve, and alleged that some of its local minima are missed when one applies the methods of infinitesimal calculus. Pierre Varignon responded by pointing out that Rolle had misrepresented the curve, and that the alleged local minima are in fact singular points with a vertical tangent.
- Barrow-Green, June (2009). "From cascades to calculus: Rolle's theorem." In: Eleanor Robson and Jacqueline A. Stedall (eds.), The Oxford handbook of the history of mathematics, Oxford University Press, pp. 737–754.
- Blay, Michel (1986). "Deux moments de la critique du calcul infinitésimal: Michel Rolle et George Berkeley." [Two moments in the criticism of infinitesimal calculus: Michel Rolle and George Berkeley] Revue d'histoire des sciences, v. 39, no. 3, pp. 223–253.
- Grcar, Joseph F. (2011), "How ordinary elimination became Gaussian elimination", Historia Mathematica 38 (2): 163–218, arXiv:0907.2397, doi:10.1016/j.hm.2010.06.003
- Rolle, Michel (1690). Traité d'Algebre. E. Michallet, Paris.
- Rolle, Michel (1691). Démonstration d'une Méthode pour resoudre les Egalitez de tous les degrez.
- O'Connor, John J.; Robertson, Edmund F., "Michel Rolle", MacTutor History of Mathematics archive, University of St Andrews.
- Michel Rolle Biography