On Numbers and Games, Hardback Book
5 out of 5 (1 rating)


ONAG, as the book is commonly known, is one of those rare publications that sprang to life in a moment of creative energy and has remained influential for over a quarter of a century. Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory.

By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers, that includes both real numbers and ordinal numbers.

These surreal numbers are applied in the author's mathematical analysis of game strategies.

The additions to the Second Edition present recent developments in the area of mathematical game theory, with a concentration on surreal numbers and the additive theory of partizan games.


  • Format: Hardback
  • Pages: 256 pages, 130 Illustrations.(some col.).
  • Publisher: Taylor & Francis Inc
  • Publication Date:
  • Category: Game theory
  • ISBN: 9781568811277



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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.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.