Knuth on Conway? Obviously you're going to love it. This book changed my life, you should read it too.

This was a good concise review! The book itself is surreal.

One thing worth pointing out that is Knuth wrote it just as the characters described: he had only a vague memory of the initial axioms that Conway had told him, so the characters' discovery matches his own process. (He wanted to illustrate how research is done, how new things in mathematics are discovered.) He gave himself a week during his sabbatical year, just locked himself in a hotel in Norway, wrote it over 6 days, “and on the seventh day he rested”. (Though he later took another week to rewrite the whole book as he had made a mistake in the axioms.) He tells the story here (see 40–42): https://www.youtube.com/watch?v=lICebKDaZRU&list=PLVV0r6CmEs...

And this book was published before Conway published anything about surreal numbers, so surreal numbers are probably the only mathematical concept whose first publication was as a book of fiction. The name “surreal numbers” also comes from Knuth (while Conway simply called them “numbers” — he later came around to agreeing that this was a good name).