I'm really interested in John Conway's work on games and I want to spend my winter reading something of his but I'm not sure between "On Numbers and Games" or "Winning Ways for Your Mathematical Plays", since they seem pretty similar. What are the differences between the books and which would you recommend?
2026-03-30 08:01:27.1774857687
"On Numbers and Games" or "Winning Ways for Your Mathematical Plays"?
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Winning Ways is a much longer work and has a lot more examples of applying the theory to actual games. It has some proofs of results, but the nitty-gritty foundational details of the theory are left out. For those, you have to read "On Numbers and Games" (ONAG).
ONAG is much more condensed in terms of applying the theory to actual games (of course there are still many examples there), but it develops the theory from scratch. It also has more results of theoretical interest like the algebraic structure of the surreal numbers, and the structure of infinite and infinitesimal games.
Personally, I discovered Winning Ways first, and found the theory fascinating but difficult for me to make rigorous on my own. Then later I discovered ONAG, and I think having first read WW (at least the first 2 volumes*) made ONAG easier to read.
*Here I am talking about the latest printing of WW; in the original, the first two volumes were combined into one.