On Numbers and Games is a mathematics book by John Horton Conway first published in 1976.

The material is, however, developed in a playful and unpretentious manner and many chapters are accessible to non-mathematicians.

Martin Gardner discussed the book at length, particularly Conway's construction of surreal numbers, in his Mathematical Games column in Scientific American in September 1976.

In the Zeroth Part, Conway provides axioms for arithmetic: addition, subtraction, multiplication, division and inequality.

The resulting construction yields a field, now called the surreal numbers.

The construction is rooted in axiomatic set theory, and is closely related to the Zermelo–Fraenkel axioms.

In the original book, Conway simply refers to this field as "the numbers".

The term "surreal numbers" is adopted later, at the suggestion of Donald Knuth.

In the First Part, Conway notes that, by dropping the constraint that L

The axioms for greater than and less than are seen to be a natural ordering on games, corresponding to which of the two players may win.

The remainder of the book is devoted to exploring a number of different (non-traditional, mathematically inspired) two-player games, such as nim, hackenbush, and the map-coloring games col and snort.

Given this object, axiomatic definitions for addition, subtraction, multiplication, division and inequality may be given.

The construction enables an entire zoo of peculiar numbers, the surreals, which form a field.

In the First Part, Conway abandons the constraint that L

Each player has a set of games called options to choose from in turn.

Games that are not numbers have a fourth possibility: they may be fuzzy, meaning that the first player has a winning strategy.