The Dialectic Relation Between Physics and Mathematics in the XIXth Century by Evelyne Barbin & Raffaele Pisano

Author:Evelyne Barbin & Raffaele Pisano
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

7 Conclusion

Liouville’s research had many different sources of inspiration. Until 1840 most of the inspiration came from his French peers. After that time he was increasingly inspired by his students, the authors in his journal and his German colleagues, in particular Gauss and his friends Dirichlet and Jacobi.

Until 1856 both his published papers and his unpublished research were to a large degree devoted to applied subjects such as electrodynamics, electrostatics, theory of heat and in particular celestial and rational mechanics. Moreover, many of his pure mathematical works were inspired by physics. This holds true of his theory of differentiation of arbitrary order, Sturm–Liouville theory and differential geometry. In the latter discipline the interaction went both ways: Mechanical problems and theorems gave rise to new geometric results and geometric results were applied to mechanics.

Thus Liouville’s mathematics is a very fine illustration of the close relation that existed between mathematics and physics in France in the middle of the nineteenth century.

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