“The Book of Nature is written in the language of mathematics, and its characters are triangles, circles and other geometrical figures, without which it is impossible to understand a single world of it.”

With this celebrated aphorism, Galileo sealed the alliance between mathematics and physics. And yet, writing three centuries later, Einstein appeared sceptical: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

In this book, Bernard Diu shows that although mathematics is, undeniably, an indispensable instrument for physics, it is not the foundation of physics. Illustrating his thesis with multiple examples, Diu stresses the difference between the mathematician's mathematics and the physicist's mathematics. The impeccable, abstract, pure rigour of the former is contrasted with the latter's quest for practical, instrumental effectiveness. Laurent Schwartz's admirable distribution theory has not dislodged the Dirac delta function from the physicist's mathematical toolbox.

A book that questions the hegemony of mathematics in the way physics and the sciences in general are taught in schools.

Bernard Diu is Professor Emeritus at the University Denis-Diderot-Paris-VII and a research fellow at the Laboratory of High Energy Theoretical Physics at the Jussieu Campus (Paris).

He is the author of Les atomes existent-ils vraiment ?, Traité de physique à l'usage des profanes, Les théories meurent aussi and, with Bénédicte Leclercq, of La Physique mot à mot.