Gabrio Piola and Mathematical Physics

Abstract : In the past, the term 'mathematical physics' had substantially two meanings. On one hand, it simply indicated modern physics, which considered mathematics its own language; in this sense, Galileo, Newton, Kepler, etc., were distinguished mathematical physicists. On the other hand, it pointed to the branch of science that developed in the XIX century and had enabled the solution of some specific problems governed by partial differential equations, such as, for instance, heat propagation, potential theory, theory of elasticity; in this sense Fourier, Lamé, Gauss, Piola, Beltrami, etc., stood among the most important mathematical physicists. Today the term indicates an academic discipline, practiced by mathematicians, having some principles of physical nature at its basis. The relation between mathematics and physics i.e., mathematical physics in the broad meaning has been the subject of an endless number of papers, from the historical, epistemological and 'scientific' points of view. The mathematical physics of the XIX century, potential theory, and the modern mathematical physics are only a little less investigated. Rather than giving exhaustive accounts of mathematical physics, the objective of this paper is to use some historical instances to define the meaning that the term 'mathematical physics' assumed in some selected historical periods. To begin with, the first instances of application of mathematics to physics, then the first appearance of something like modern mathematical physics, and, eventually, a particular kind of mathematical physics theory, called rational mechanics, are discussed. For the sake of brevity, the golden age of physics, ranging from Galileo to Newton, has been ignored, without preventing this paper from reaching its objective, that is, the discussion of the meaning of the discipline called mathematical physics.
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Danilo Capecchi. Gabrio Piola and Mathematical Physics. The complete works of Gabrio Piola: Volume I, 38, 2014, Advanced Structured Materials. ⟨hal-00955826⟩

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