1. Presentation

Bourbaki is certainly responsible, in France and worldwide, for the universal use of the modern language of elementary mathematics, set and structure theory. Of course, this is no more than the widespread dissemination of ideas that professional mathematicians had recognized as their own for many decades, through the teaching that Bourbaki's pupils carried out in universities and high schools. This dissemination was only made possible by the ergonomic nature of the language, which enables a variety of mathematical objects to be manipulated clearly and effortlessly.

However, we shouldn't assume that this language, which has become natural to mathematical users, has emerged fully armed from the practice of mathematicians.

• The concept of function or application, for example, was developed by trial and error over the course...