"Games", Conway, names, and meaning

"One of the most brilliant mathematicians of the last and current century is John Horton Conway. Near the middle of the last century he formalized a notion of game in terms of a certain recursive data structure. He went on to show that every notion of number that has made it into the canon of numerical notions could be given representations in terms of this data structure. These ideas are documented in his delightful On Numbers and Games. Knuth popularized some of these ideas in his writings on surreal numbers."