On Numbers and Games

John Horton Conway

Discover the captivating world of “On Numbers and Games” by John Conway! In this marvelous book, Conway explores surreal numbers and unveils a mind-boggling array of infinite and infinitesimal numbers alongside the real numbers. Overflowing with creativity and insight, it’s a must-read for any math enthusiast.

Now, after 25 years, a new edition has arrived, making this long-out-of-print gem accessible once again. While the changes are minimal, with some corrections and an insightful Epilogue discussing recent progress in studying Surreal Numbers, the book still offers intriguing ideas and thought-provoking questions for further exploration.

One of the most fascinating aspects I discovered was Conway’s revelation of the connection between numbers and combinatorial games. A number, it turns out, can be viewed as a unique kind of game. This theory is further developed in the first part of “On Numbers and Games,” with promised advancements in a subsequent volume, “Winning Ways,” co-authored by Elwyn Berlekamp and Richard Guy. “Winning Ways” continues the journey, delving into the theory of combinatorial games and applying it to an array of captivating games.

From there, the theory continued to evolve, leading to the publication of “Games of No Chance,” a collection of research from a recent workshop. And there’s more to come with a forthcoming sequel. This book acts as the gateway to an ongoing, living mathematical theory.

The new edition of “On Numbers and Games” splits the original two-volume set into four, providing readers with the first volume of this comprehensive work. While lightly revised, the authors have included exciting “Extras” at the end of each chapter, along with references to recent advancements. With stunning color images sprinkled throughout, it’s a joy to have this beautifully produced book back in print.

Don’t miss out on the opportunity to explore the enchanting world of “On Numbers and Games” and delve into the groundbreaking theories of John Conway.