The tools of optimization

One of the great strengths of mathematics is the ability to question the language in which they are written: which word to choose to name an abstract concept? How to express an idea so that the vocabulary used does not slow down its assimilation? Better yet: mathematics can also take language itself as an object of study! From this approach stems the modern theory of information: formal languages, programming…

Visual, surprising and rich in applications (the structure of the football is the most well-known), it features in the pantheon of the most beautiful mathematical formulas: V + F = E + 2. While the study of polyhedra already fascinated Plato, the relationship connecting the number of its vertices, its faces and its edges had been anticipated by Descartes before being rigorously expressed by Euler, the Swiss mathematician who gave it his name (it's only fitting!). Poincaré undertook to generalize it, but it is still far from having revealed all its secrets.

Human activity is subject to constraints of all kinds: material, human, financial, spatial, temporal… This limitation of resources explains why a large part of "applied mathematics" consists of optimizing a criterion under certain constraints. This targeted dossier proposes to explore a lesser-known and non-technical facet of optimization: yes, without sophisticated analytical machinery, with only a good understanding of simple algebraic or geometric concepts, one can already obtain astonishing results!