John Horton Conway (1937–2020)

Have you ever exploited symmetry in your own designs, proofs, or organizational solutions? Of course the answer is "yes": symmetry is one of the deepest principles of human mind. In the form of conservation laws, it literally provides the basis for much of modern physics. But don't worry, this book is not about physics! It is a heavily illustrated book about the math behind symmetry.

Conway has created a wonderful example of graphical clarity and geometric thinking about regular patterns and tilings. Don't be put off by his coinage of goofy terms; he successfully presents deep mathematics via purely visual proofs. Furthermore, he turns the old way of presenting symmetry on its head, starting with geometry and topology, and only later addressing group theory.

This book is highly recommended to anyone who is interested in how symmetry works. Some understanding of group theory would be helpful, but the graphics alone make perusing the book worthwhile.… (more)

I read the first edition of this book as an undergraduate student of mathematics and, like many of my peers, was astonished at the effortless way in which an entire new class of numbers was defined, and then extended again to embrace the world of mathematical games. It's deep, yet playful (anything which deals with 'surreal numbers' is OK by me) and accessible, although not to someone without some knowledge of algebra. Conway is an inventive genius and nowhere is that more obvious than in this book.
(The copy catalogued here is the second edition of 2001; the original dates from 1976, when I first read it.)
This ranks with "Mathematics made difficult" and most of Martin Gardner's mathematical diversions as essential reading for enthusiasts of mathematics. It reminds you why it's fun.… (more)