Work
Rolle was an early critic of infinitesimal calculus, arguing that it was inaccurate, based upon unsound reasoning, and was a collection of ingenious fallacies, but later changed his opinion.
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.
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