You might be taken aback if someone were to tell you that mathematics can have a very beautiful side. But you should be aware that there are those people who spend their entire life doing mathematics and who develop mathematics in the same way that a composer makes music. In most cases, when a mathematician finds a solution to a problem, this results in the creation of many more problems that are fresh and stunning in the same way that the original problem was. Of course, a lot of the time, these issues are pretty challenging, and, just like in other fields of study, they can only be comprehended by individuals who have researched the topic extensively and have a solid grasp of the material.

In 1981, Jean Brette, who was in charge of the Mathematics Section at the Palais de la Decouverte (formerly known as the Paris Science Museum), invited me to present at the Palais. I had never before presented such a conference to an audience that was not familiar with mathematics. This presented me with a challenge: was it possible for me to explain to such a large audience on a Saturday afternoon what it meant to practice mathematics and why one does mathematics?

When I refer to mathematics, I mean purely mathematical concepts. This does not imply that pure mathematics is superior to other forms of mathematics; however, since a few other people and I are involved in pure mathematics, I am now worried about those individuals. Math has a poor reputation, which may be traced back to the earliest levels of education. The term is put to use in a wide variety of settings. To begin, I was required to provide a brief explanation of these potential contexts, as well as the one with which I intended to engage.