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Etienne Ghys Director of Research at the CNRS, Professor at the École Normale Supérieure de Lyon Permanent Secretary of the French Academy of Sciences It is unusual for a mathematical idea to spread throughout society. However, this is the case with chaos theory, popularized thanks to the butterfly effect, imagined by the American meteorologist Edward Lorenz who, in 1972, asked the famous question: "Does the flapping of a butterfly's wings in Brazil trigger a tornado in Texas?" The idea in this image is that a small cause can have large consequences. But can chaos theory be summarized in such a simplistic way? Can a scientific theory be satisfied with negative statements? Are mathematicians responsible for the inadequate transmission of this theory? This conference will attempt to address these questions and, in particular, to describe the positive side of the theory. Because there are some. Indeed, chaos sometimes gives rise to a kind of order. Chaotic systems may be unpredictable, but they are far from incomprehensible.