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1. Abstract on: History and Epistemology of Science [Emeritus Prof. Dhombres, France]

Start Date:
11. October 2017, 08:45
Finish date:
11. October 2017, 09:45
École Dotorale Lille 3 University



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



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 20th 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 20th 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.



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