The regularities of prime numbers and Fermat's theorem, Poincaré's hypothesis and Kepler's spherical symmetry, the mystery of the number , and orbital chaos in celestial mechanics. Many of us have only heard from the edge of our ears about the mysterious and incomprehensible mysteries of modern mathematics. Meanwhile, paradoxically, the fundamental goal of this science is to reveal the inner simplicity of the most complex questions. English mathematician and science popularizer, Professor Ian Stewart, helps the reader overcome the psychological barrier. Fascinating and accessible, he talks about the most difficult tasks that the greatest minds have fought and continue to fight over, the origins of such problems, why they are so important and what place they occupy in the general context of mathematics and natural sciences. This book is a guide to the amazing and mysterious world of numbers, theorems and hypotheses, to the forefront of mathematical science, which is trying to solve the problems posed to it thousands of years ago by new methods.