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Michel Rolle (April 21, 1652 – November 8, 1719) was a French mathematician. He is best known for Rolle's theorem (1691).


Rolle was born in Ambert, Basse-Auvergne. In 1675, he moved from Ambert to Paris and was elected in 1685 to join the Académie Royale des Sciences. He became a Pensionnaire Géometre of the Académie (1699). He had then already been given a pension by Jean-Baptiste Colbert after he solved one of Jacques Ozanam's problems.

Rolle was an early critic of infinitesimal calculus, arguing that it was inaccurate, based upon unsound reasoning, and was a collection of ingenious fallacies,[1] but later changed his opinion.[2]

In 1690 he was the first person to adopt Albert Girard's 1629 suggestion for the current standardized notation for the n-th root of a number \displaystyle x, placing the number n within the radical sign:[3][4]

Rolle died in Paris.

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 a specific algebraic curve, and alleged that some of its local minima are missed when one applies the methods of infinitesimal calculus. Johann Bernoulli 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.


1. ^
2. ^
3. ^ See Table of mathematical symbols by introduction date and Earliest Uses of Symbols of Operation: «Placement of the index within the opening of the radical sign was suggested in 1629 by Albert Girard (1595-1632) in Invention nouvelle. He suggested this notation for the cube root... the first person to adopt Girard's suggestion and place the index within the opening of the radical sign was Michel Rolle (1652-1719) in 1690 in Traité d'Algèbre.»
4. ^ Florian Cajori, A History of Mathematical Notation, pp 371-2.

External links

* O'Connor, John J.; Robertson, Edmund F., "Michel Rolle", MacTutor History of Mathematics archive, University of St Andrews, .
* Michel Rolle Biography

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