Principles of prime numbers and Fermat’s theorem, Poincare’s hypothesis and Kepler’s spherical symmetry, the mystery of the number π and orbital chaos in celestial mechanics. Many of us have only heard 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 issues. English mathematician and science popularizer, Professor Ian Stewart, helps the reader overcome the psychological barrier. In a fascinating and accessible way, he talks about the most difficult problems that the greatest minds have struggled and continue to struggle with, about the origins of such problems, why they are so important and what place they occupy in the general context of mathematics and the 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 problems posed to it thousands of years ago using new methods.