"'The important thing is not to stop questioning': the relevance of this Einstein quote in natural sciences is exemplified in physics and related mathematics" Daniel Sternheimer

Title:  "The important thing is not to stop questioning": the relevance of this Einstein quote in natural sciences is exemplified in physics and related mathematics.

Speaker: 

Daniel Sternheimer
Visiting Research Fellow, Rikkyo University, Tokyo

Modern science is a Babel tower, the foundations of which are too often forgotten. Yet revolutions may occur when one takes seriously an essential question: "Is it necessarily so?" Indeed a successful model is based on assumptions that are sufficient to explain existing data, but may not be necessary. That is the mathematical curse of experimental sciences, since one tends not to argue with success (or with what one has been taught) unless one is forced to.

In 1960 Wigner (who in 1963 got the Nobel Prize in physics for "the discovery and applications of fundamental symmetry principles") marvelled about "the unreasonable effectiveness of mathematics in the natural sciences," referring mainly to physics.

We shall exemplify all this by first briefly explaining how a posteriori relativity and quantum mechanics can be obtained from previously known theories using the mathematical theory of deformations. Then we describe some main features of the standard model of elementary particles and how it arose from empirically guessed symmetries. Finally we indicate how, questioning its foundations, its symmetries might be obtained from those of relativity using deformations (including quantization), which poses hard mathematical problems and might eventually question half a century of particle physics.