This mini‑book is a fascinating journey through paradoxes that challenge logic, from Hilbert’s hotel which makes room for an infinity of extra guests to the liar’s puzzle and the impossible Penrose “tribar.” Structured like a research article with clear sections, it explores paradoxes of infinity, probability, electoral cycles and social phenomena while presenting the most recent scientific advances (2024‑2025) on topics ranging from the black‑hole information paradox to closed timelike curves that could enable paradox‑free time travel. Each chapter draws on academic studies and articles from reliable sources to explain why intuitive reasoning is often undone by rigorous demonstrations.

Readers will discover how the birthday paradox overturns our intuition about sharing a birth date, how two losing games can lead to a winning strategy (Parrondo’s paradox), why most of our friends have more friends than we do (the friendship paradox) and how AI algorithms can encounter logical limits inherited from Gödel and Turing. The book also discusses economic paradoxes such as Jevons’s paradox in the context of AI and cosmological paradoxes like the mystery of extraterrestrial life. Rich in concrete examples and reading suggestions, it is an accessible yet demanding introduction to the beauty of paradoxical reasoning.

Publisher : Five Minutes – Collection : SAVOIR EN BREF. Dive into these paradoxes and prepare to be surprised : each page invites you to reconsider your certainties and to savor the power of mathematical thought. Perfect for anyone who wishes to understand the ideas that shake the scientific community while enriching their general knowledge.