This article records tradition as it has been passed down and reported. Its sources are not yet part of the atlas's verified catalogue.
In the early 1970s, the mathematician John Conway spent a lot of time at Cambridge watching strong Go players finish their games. He was not trying to get better at Go. He was trying to understand something odd about how those endgames worked: late in a game of Go, the board effectively splits into several small, separate local fights, and a player has to decide which fight to play in next. Conway noticed that each of these local positions could be compared to the others in a way that looked exactly like comparing numbers, even though nothing about a Go endgame looks like arithmetic on the surface.
He followed the idea all the way down. If a game position could be treated as a kind of number, what happens if you define numbers themselves as game positions, built recursively from earlier, simpler positions? The answer turned out to be a genuinely new number system. Conway's construction did not just reproduce the ordinary integers and fractions. It also generated infinite numbers, infinitesimal numbers smaller than any positive real number yet still greater than zero, and vast further reaches beyond both. Donald Knuth later gave this construction a name, the surreal numbers, in a short 1974 book written as a dialogue between two students discovering the idea for themselves.
Conway published the full theory himself in 1976, in a book called On Numbers and Games, and the broader framework it introduced, treating games as mathematical objects with their own values, sums and comparisons, became known as combinatorial game theory. It is a different kind of game theory from the one John von Neumann and John Nash had built decades earlier for economics and strategic decision making. Von Neumann and Nash studied games with hidden information or simultaneous choices, where the interesting question is what a rational opponent will do. Conway's games have no hidden information and no element of chance at all, Go, checkers, Nim, and the interesting question is instead what a position is worth, treated as a strange kind of arithmetic in its own right.
Conway went on to a career that touched an unusual number of separate fields, from finite group theory to the invention of the cellular automaton called the Game of Life, but he described On Numbers and Games as the work that gave him a system, not just a scattering of results, and its origin remained the same throughout: a mathematician watching a board game closely enough to see the numbers hiding inside it.