Michel role

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Michel Rolle (born April 21, 1652 in Ambert , Basse-Auvergne , † November 8, 1719 in Paris ) was a French mathematician and member of the Académie des Sciences .

Treatise on Algebra by Rolle 1690

Rolle was the son of a shopkeeper and was essentially self-taught. He worked as an assistant to a notary and for various lawyers before moving to Paris in 1675, where he married soon afterwards. He built himself a reputation as a mathematician and in 1682 received a reward from Jean-Baptiste Colbert for solving a number theoretic problem posed by Jacques Ozanam . Colbert also procured him a small pension and the War Minister François-Michel Le Tellier, marquis de Louvois hired him as a math teacher for one of his sons ( Camille Le Tellier de Louvois ) - another small post in the War Ministry was not to Rolles' taste, so that he soon gave it up again. Under the influence of Louvois, he also became a member of the French Academy of Sciences in 1685. In 1699 he became a pensioner Géometre of the academy. In 1708 he suffered a stroke and afterwards did not publish any more mathematical works.

Rolle was primarily an algebraist who also dealt with Diophantine equations in number theory. In 1690 his treatise on Algebra Traité d'algèbre was published , in which he also introduced the symbol for the nth roots that is common today. He also pushed through other mathematical notations, such as the usual symbol = for equality, previously introduced by Robert Recorde , but not generally used at the time.

In the analysis known is the eponymous set of roller (1,691) on differentiable functions . This theorem of analysis has its origin for Rolle in a more comprehensive algebraic theory, which he called the theory of cascades and which essentially consisted in the transition from a polynomial to its derivation, although Rolle himself did not yet use any terms from infinitesimal calculus. He even refused it because, in his opinion, it did not provide any new truths and, on the contrary, was even flawed (compared to the algebraic methods of Pierre de Fermat and Johann van Waveren Hudde ). With George Berkeley he was one of the early critics of the foundation of analysis. Rolle proved the theorem named after him purely algebraically for polynomials. Rolle proved it in the form that between two zeros of a polynomial there is a zero of the derivative of the polynomial. Augustin Louis Cauchy published a general proof in 1823 under the mean value theorem . The sentence was named after Rolle in the 19th century ( Moritz Wilhelm Drobisch 1834, Giusto Bellavitis 1860, Joseph Serret , Höhere Algebra, Volume 1, 1868, p. 216). The main goal of Rolle was to determine the roots of algebraic equations, which he narrowed down with the help of his cascade method (that is, by considering the derivatives of the polynomials). In his Traité d'algèbre he also deals with Diophantine equations.

From 1700 to 1701 there was a heated argument between Rolle and Pierre Varignon about the analysis introduced by Gottfried Wilhelm Leibniz and Isaac Newton at the Paris Academy of Sciences . After no agreement could be reached at the academy, Rolle continued the argument in the Journal des sçavans , but in the end admitted his mistake.

literature

  • Jean Itard , Article Rolle in Dictionary of Scientific Biography
  • P. Mancosu: The metaphysics of the calculus: a foundational debate in the Paris Academy of Sciences, 1700-1706, Historia Math., Vol. 16, 1989, pp. 224-248.
  • J. Shain: The Method of Cascades, Amer. Math. Monthly, Vol. 44, 1937, pp. 24-29.
  • Florian Cajori: On Michel Rolle's book "Méthode pour resoudre les égalitez" and the history of Rolle's theorem, Bibliotheca Mathematica, 1911, pp. 300-313

Web links

Individual evidence

  1. ↑ 1846 by Giusto Bellavitis
  2. ↑ Published in Démonstration d´une Méthode pour resoudre les Egalitez de tous les degrez , Gallica . These were intended to complete his Traité d'algèbre of 1690 and to provide missing evidence.
  3. ↑ Role You nouveau système de l'infini , 1703
  4. ↑ a b Florian Cajori: On Michel Rolle's book "Méthode pour resoudre les égalitez" and the history of Rolle's theorem, Bibliotheca Mathematica, 1911, pp. 300-313
personal data
SURNAME Role, Michel
BRIEF DESCRIPTION Member of the Academie des Sciences
DATE OF BIRTH April 21, 1652
PLACE OF BIRTH Ambert , Lower Auvergne
DATE OF DEATH November 8, 1719
Place of death Paris