**Michel Rolle** was a French mathematician best known for the so-called Rolle's theorem.

- Michel had little formal education being largely self-educated after receiving some elementary schooling.
- Jean-Baptiste Colbert, the controller general of finance and secretary of state for the navy under King Louis XIV of France, rewarded Rolle for this achievement.
- Rolle was hired by Louvois, who came to be greatly impressed by his pedagogic and mathematical skills.
- From 1783 onwards Louvois was in a position to confer further scientific patronage on his protégé and did so when he made Rolle a member of the Académie in 1685.
- Ozanam stated that the smallest of the four numbers with these properties would have at least 50 digits, but Rolle found four numbers satisfying the conditions with each number having seven digits.
- Louvois, who is referred to in the above quote, was François Michel le Tellier, Marquis de Louvois, the French Secretary of State for War.
- He employed Rolle to tutor his fourth son, Camille le Tellier (1675-1718).
- The Marquis de Louvois arranged for Rolle to have an administrative post in the Ministry of War, but Rolle disliked the work and soon resigned.
- Rolle was elected to the Académie Royale des Sciences in 1685 and the impressive mathematical work he produced following his election fully justified the Marquis de Louvois' faith in him.
- Before going on to discuss the interesting mathematical contributions Rolle made, let us give a couple of further facts about his life.
- In 1708 Rolle suffered a stroke.
- Let us now look at Rolle's important mathematical contributions.
- In Traité d'algèbre Ⓣ(Treatise on algebra) Rolle used the Euclidean algorithm to find the greatest common divisor of two polynomials.
- Rolle then constructs the 'second cascade' which is the second derivative, and continues in this fashion.
- Rolle's theorem, an important proposition of the calculus, also owes its origin to the method.
- Rolle is best remembered for 'Rolle's Theorem' which was published in Démonstration d'une Méthode pour resoudre les Egalitez de tous les degrez Ⓣ(Demonstration of a method for solving equations of all degrees) in 1691.
- The name 'Rolle's Theorem' was given to this basic result by Giusto Bellavitis in 1846.
- In his 1691 work Rolle adopted the notion that if a>ba > ba>b then −b>−a-b > -a−b>−a.
- Rolle published another important work on solutions of indeterminate equations in 1699, Méthode pour résoudre les équations indéterminées de l'algèbre Ⓣ(Method for solving indeterminate algebraic qquations).
- It might be assumed from what we have just written about Rolle's work that he was developing the infinitesimal calculus.
- This would be a serious error, for Rolle described the infinitesimal calculus as a collection of ingenious fallacies and he believed that the methods could lead to errors.
- This vigorous disagreement was between Rolle and Pierre Varignon and it ended in uproar (some say that Rolle's lack of breeding showed in his bad behaviour).
- For example, Rolle addressed the Academy on 12 March and 16 March 1701.
- This is a cleverly constructed example, but Varignon was able to see the subtle error in Rolle's analysis.
- After the Academy decided that no further discussion of this topic was take place, Rolle continued the argument in the pages of the Journal des sçavans opposed by Joseph Saurin.
- To his eternal credit, Rolle eventually conceded that he was wrong.

Born 21 April 1652, Ambert, Basse-Auvergne, France. Died 8 November 1719, Paris, France.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive