The objective of this paper is to use some historical instances to explain in detail the meaning of mathematical physics theories in selected historical periods. The paper presents, in order, the first instances of applications of mathematics to physics, the first appearance of something resembling modern mathematical physics and a particular kind of mathematical physics theory, called rational mechanics. At the end of the paper, epistemological considerations clarify the difference between physical, mathematical, and mathematical physics theories.
Aristotle. Analytica posteriora. Translation into English by Mure GRG and Gaye RK. The Tech Classics Archive of M.I.T., 1994–2009.
2.
CorbiniA. La teoria della scienza nel XIII secolo. I commenti agli analitici secondi. Firenze: Edizioni del Galluzzo, 2006.
3.
TarantinoP. La trattazione aristotelica delle scienze subordinate negli Analitici secondi. Rivista di storia della filosofia2012; 3: 445–469.
4.
Aristotle. Physica, Translation into English by Hardie RP and Gaye RK. The Tech Classics Archive of M.I.T., 1994–2009.
5.
Aristotle. Metaphysica. Translation into English by Ross WD. The Tech Classics Archive of M.I.T., 1994–2009.
6.
Aristotle. Mechanical problems. In: HettWS (ed.), Aristotle. Minor works. Cambridge: William Heinemann, 1955.
7.
LennoxJG. Aristotle, Galileo and the mixed sciences. In Reinterpreting Galileo. Washington, DC: William Wallace, 1985, pp. 29–51.
8.
FourierJ. Théorie analytique de la chaleur. Paris: Firmin-Didot, 1822.
9.
LaméG. Leçons sur la théorie mathématique de l’élasticité des corps solides. Paris: Mallet-Bachelier, 1852.
10.
LaméG. Leçons sur les fonctions inverses des transcendantes et les surfaces isotherme. Paris: Mallet-Bachelier, 1857.
11.
LaméG. Leçons sur les coordonnées curvilignes et leurs diverses applications. Paris: Mallet-Bachelier, 1859.
12.
LaméG. Leçons sur la théorie analytique de la chaleur. Paris: Mallet-Bachelier, 1861.
13.
PisanoRCapecchiD. La théorie analytique de la chaleur. Notes on Fourier and Lamé. Sabix2009; 44: 87–93.
14.
LaméG. Note sur la marche ŝuivre pour découvrir le principe seul véritablement universel de la nature physique. C R Acad Sci Paris1863; 56: 983–989.
15.
BarbinEGuitartR. Mathematical physics in the style of Gabriel Lamé and the treatise of Emile Mathieu. In: BarbinEPisanoR (eds), The dialectic relation between physics and mathematics in the XIXth century. Dordrecht: Springer, 2013.
16.
SchloteKH. The emergence of mathematical physics at the university of Leipzig. In: BarbinEPisanoR (eds), The dialectic relation between physics and mathematics in the XIXth century. Dordrecht: Springer, 2013.
17.
LagrangeJL. Theorie de la libration de la Lune (1780). In: SerretJADarbouxG (eds), Oeuvres de Lagrange, vol. 5. Paris: Gauthier-Villars, 1867–1892, pp. 5–124.
LaplacePS. Traité de mécanique céléste, Vol. 1. Paris: Duprat, 1829.
20.
LaplacePS. Théorie des attractions des sphéeroїdes et de la figure des planètes. In: Mémoires de l’Académie des sciences de Paris. Paris: l’Académie des sciences de Paris, 1782, pp. 113–196.
21.
EulerL. Principia motus fluidorum (1753). N Comm Acad Petropolitanae1761; 6: 271–311.
22.
PoissonSD. Rémarques sur une équation qui se présente dans la théorie des attractions des sphéroodes. N Bull Soc Philomat Paris1813; 3: 388–392.
23.
GaussCF. Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhältnisse wirkenden Anziehungs- und Abstossungskräfte. In Gauss CF (1863–1933) Werke, Vol. 5. Göttingen, 1840, pp. 194–242.
24.
CapecchiDRutaGTazzioliR. Enrico Betti: Teoria del potenziale. Benevento: Hevelius, 2006.
25.
GreenG. An essay of the application of the mathematical analysis to the theories of electricity and magnetism (1828). In: Mathematical Papers of the late George Green. London: McMillan and co., 1871, pp. 1–82.
26.
GreenG. On the determination of the exterior and interior attractions of ellipsoids of variable densities (1835). In: Mathematical Papers of the late George Green. London: McMillan and co., 1871, pp. 187–222.
27.
KlineM. Mathematical Thought from Ancient to Modern Times. Oxford: Oxford University Press, 1972.
28.
WeierstrassK. Über die sogenannte Dirichlet’sche Princip. In: Mathematische Werke, Vol. 2, Berlin, 1895, pp. 49–54.
29.
TazzioliR. Green’s function in some contributions of 19th century mathematicians. Historia Mathematica2001; 28: 232–252.
30.
HilbertD. Über das Dirichletsche Prinzip. Math Ann1904; 59: 161–186.
31.
HilbertD. Über das Dirichletsche Prinzip. J reine angew Math1905; 129: 63–67.
32.
CarnotL. Principes fondamentaux de l’équilibre et du mouvement. Paris: Deterville, 1803.
33.
TruesdellCA. Essay in the History of Mechanics. New York: Springer, 1968.
