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Michel RolleFrench mathematician
Date of Birth: 21.04.1652
Country:  France |
Content:
Biography of Michel Rolle
Michel Rolle, a French mathematician, was born in the town of Ambert in the province of Auvergne. At the age of 23, he moved to Paris where he initially supported himself through correspondence. His mathematical knowledge, particularly demonstrated in solving a difficult problem proposed by Ozanam, opened the doors for him to join the academy in 1685.
Academic Career and Controversies
Rolle's academic career was marked by heated attacks on differential calculus and Descartes' analysis. In 1701, he strongly objected to the logical foundations of differential calculus and the results achieved by Descartes. Varignon exposed the errors made by Rolle in his refutation and provided a true understanding of differentials. In 1702, Rolle published a new article against differential calculus in the "Journal des Savans." This time, his arguments were countered successfully by Saurin. In 1705, the academy acknowledged Rolle's errors, a fact later accepted by Rolle himself.
A dispute between Rolle and Abbe de Gua arose regarding Rolle's attacks on Descartes' analysis. Rolle's polemical writings were full of errors and characterized by obscure explanations. Among his works related to differential calculus, published in the memoirs of the Paris Academy, are "Remarques sur les lignes géométriques" (1702 and 1703), "Du nouv. système de l'infini" (1703), "De l'inverse des tangentes" (1705), and "Observations sur les tangentes" (1705).
Despite the disregard towards Rolle's controversy on differential calculus, it compelled Leibniz and his supporters to pay greater attention to the logical foundations of the subject. Rolle's contributions extended beyond calculus. He developed a method for solving indeterminate equations of the first degree in whole and positive numbers, surpassing his predecessor, Bache de Meziriac. This method, along with its applications, can be found in his "Traitè d'Algèbre" (1890) and a separate work titled "Méthodes pour résoudre les questions indéterminées de l'Algèbre" (1699), which also discusses indeterminate equations of higher degrees. This method is now known as "Maclaurin's Rule."
Numerical Solutions and Rolle's Theorem
Rolle's work on numerical solutions of equations, particularly his method of cascades for determining the limits enclosing the root of an equation, is even more significant. He formulated the theorem that states "between two consecutive roots of the equation f'(x) = 0, there can be at most one root of the equation f(x) = 0." Rolle's research on these topics can be found in his "Traitè d'Algèbre" and "Sur les effections géométriques" (Paris, 1690). Noteworthy chapters in his "Traitè d'Algèbre" include the search for the greatest common divisor of two polynomials forming an equation and the theorem on the number of values of the nth degree root.
Despite the importance of Rolle's research, some of it went unnoticed by his contemporaries and was only recognized much later. Nonetheless, his contributions stimulated greater attention to the logical foundations of new mathematical concepts, making him an influential figure in the development of mathematics.
