This book is not just another ordinary manual, as it aims to make the reader fully understand the fundamental mathematic principles that students often learn without really knowing what they signify. Beyond the formalism of our teaching, the intention is to reconstitute the underlying intuition which has inspired the formulation of these principles and which alone renders them intelligible. In the first section of this work, the author develops his conception of mathematics as a science which derives from concrete observations, not from purely mental calculation. The second part uses the most intuitive approach possible to examine these ten principles, from the theorem of Thalès to differential forms – in other words from the origins of geometry to the formalism of modern physics.

Claude-Paul Bruter is a professor at the University of Créteil. He is the author of numerous works on the teaching and philosophy of mathematics, and notably wrote the introduction to the theory of catastrophes of René Thom : Topologie et Perception, vol. 1.