The interaction of physics, mechanics and mathematics in Joseph Liouville's research

• Autores: Jesper Lützen
• Localización: The Circulation of Science and Technology: Proceedings of the 4th International Conference of the European Society for the History of Science. Barcelona, 18-20 November 2010 / coord. por Antoni M. Roca Rosell, 2012, ISBN 978-84-9965-108-8, págs. 520-521
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • According to Joseph Liouville, mathematics owes its most important progress to physics, and in particular to mechanics. In fact, many of his own most important research was directly or indirectly inspired by physical problems. In the talk I shall exemplify the physical origin of some of Liouville’s theories and results. Some of them are surprising. For example, it is rather surprising that his theory of differentiation of arbitrary order (fractional calculus) was a result of his attempt to find elementary forces in a Laplacian approach to physics, and that his celebrated theorem about the constancy of volume in phase space was inspired not by thermodynamics but by perturbation theory in celestial mechanics. I shall also show the close link existing between Liouville’s research in mechanics and his research in differential geometry.

    The talk will exemplify the close links between mathematics and physics in France at the beginning of the 19th century