Abstract
The relationship between mathematics and empirical science has evolved and developed historically, and is continuing to evolve and develop today. The twentieth century has seen many new and different ways in which mathematics is used, in non-linear analysis, computer science, operations research, industrial engineering, economics, and so forth. The present paper discusses some aspects of the interaction of mathematical analysis and theoretical mechanics during the period 1700–1900, with attention to the relatively classical example of the calculus of variations on the one hand, and Hamilton-Jacobi theory on the other.
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Fraser, C. (2000). Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations: A Study in the Interaction of Mathematics and Physics. In: Grosholz, E., Breger, H. (eds) The Growth of Mathematical Knowledge. Synthese Library, vol 289. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9558-2_7
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