Title

What has Fourier changed on a long term in the roles of models in mathematical physics?

Abstract

Historical epistemology of science has also to take care of reception of some given scientific work on the long term up to now, and of the transformation of concepts, theories, and even tools an author invented. One of the main difficulty in this task is to differentiate between what historians have studied by looking essentially on published texts or on manuscripts of an author, from what successors as scientists did in their own ways about some parts of this author’s work. Moreover there is the role of textbooks, and a reception cannot always be called posterity. I wish to raise this sort of historiographical question by looking at Fourier, and his physico-mathematical work on heat propagation, published in 1822, but almost entirely written in 1807. Intertwined between physics and mathematics, there are many concepts (the flux of heat for example, or the proper modes of heat propagation) and models (the lamina model that provided the Fourier series, or the differential parallelepiped to obtain the partial differential equation of heat) that may be distinguished among Fourier’s achievements. And there is the Fourier transform as we call it today. Did they become tools, objects, domains in themselves? How have they been generalized, modified, criticized, and the example of wavelets developed at the end of the 20^th century is an essential example here. Can we do serious historical epistemology with such a large run of time? May we be able to separate the influence on physics (Maxwell was describing Fourier‘s work as a poem) and on mathematics where Fourier for sure is responsible for the idea of representation, implying functional analysis developed during the 20^th century only.

My aim then is to argue that the astonishing resources of the web, with the ability to cover so various sources and so many explanations, and errors as well, may just be a sort of experimental way to teach mathematics. I would like to do so on two examples only, to be able to conduct some critical discussion. I’ll choose Kepler’s third law and Descartes’ rule of signs.

References

• Charbonneau L (1994) Catalogue des manuscrits de Joseph Fourier conservés au cabinet des manuscrits de la Bibliothèque Nationale (fonds français 22501 à 22529), Paris. Presses de l’Université de Nantes pour la Société française d’histoire des sciences et des techniques. Cahiers d’histoire & de philosophie des sciences, nouvelle série 42
• Dhombres J, Robert JB (1998) Joseph Fourier, créateur de la physique mathématique. Paris. Belin
• Fourier JBF (1888–1890) Œuvres de Fourier par les soins de M.  Gaston Darboux. 2 vols. Paris. Gauthier–Villars
• Grattan-Guinness I (1990) Convolutions in French mathematics, 1800-1840. Science Networks. Basel. Birkhäuser
• Grattan-Guinness I, Ravetz JR (1972) Joseph Fourier 1768-1830. A survey of his life and work, based on a critical edition of his monograph on the propagation of heat, presented to the Institut de France in 1807. MIT Press. Cambridge, MA.
• Herivel J (1980) Joseph Fourier. Face aux objections contre sa théorie de la chaleur, Lettres inédites 1808-1816. Paris. CTHS. Bibliothèque Nationale
• Fox R (1974) The rise and fall of Laplacian physics, Historical Studies in the Physical Sciences 4:89–136.
• Maxwell JC (1873) A Treatise on Electricity and Magnetism, 2 vols. The Clarendon Press, Oxford
• Pisano R, Bussotti P (2017) The Emergencies of Mechanics and Thermodynamics in the Western Society during 18th–19th Century. In: Pisano R, (ed). A Bridge between Conceptual Frameworks, Science, Society and Technology Studies. Springer. Dordrecht, pp. 399-436

Contact

jean.dhombres@cnrs.fr