Some paradoxes to think about

A situation is generally described as "paradoxical" without really knowing what the notion of paradox means. If this word is vague, it is because the concept of paradox can take on many meanings, particularly in mathematics: a result that seems absurd, a result that seems to go against a theory, or even a situation where one no longer knows what to conclude. The common point of all these meanings is the astonishment one feels, an astonishment that is beneficial for the mind because it forces one to ask questions: have I been fooled by my intuition? This will be the case with Simpson's and Penney's paradoxes. Will I be able to find a convincing answer? We will see this with the two envelopes paradox. Does the conceptual framework of the problem have a blind spot? This will be the adventure of Allais's paradox. We will end with the aperitif...

Mandelbrot understood that, far from being mere mathematical curiosities, fractals, these self-similar objects, could constitute a powerful description of vast fields of the real world. Thus he offered a new perspective on an entire branch of mathematics, while showing how relevant fractal models could be for the study of nature or for modeling stock market fluctuations. But if Benoît Mandelbrot's name is associated with fractals, particularly the one bearing his name, we often forget that he also worked in many other fields: aerospace, information theory, linguistics…