# Genius At Play

> Source: https://ollybritton.com/notes/books/genius-at-play/ · Updated: 2026-02-07 · Tags: book

![genius-at-play.jpg](https://ollybritton.com/assets/attachments/img/genius-at-play.jpg)

> Biography about the life and work of John Horton Conway.

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I thought this was really good! I listened to the audiobook version and it was just maths-y enough to be understandable without actually having a paper copy in front of me (though I did refer to the accompanying PDF a few times).

It was a really nice mix between finding out about John Conway himself, looking at actual concepts like the surreal numbers and groups, and a higher-level commentary on mathematics in general.

### The nature of mathematical existence
> I’ll tell you what interests me about this—it’s really what interests me about mathematics. Nobody else in the whole history of the world has been stupid enough to invent this rule. That’s the first thing. But then, if they had, they would find exactly this behaviour that I’m finding.
> 
> [...]
> 
> And, how can I say it, even though nobody’s ever looked at it—and I’m absolutely sure that nobody’s ever looked at it; I mean, it’s not inconceivable that somebody’s invented it, but why the hell should they have, you know?—but if they had, they would have found this.
> 
> That’s a curious thing about the nature of mathematical existence. This rule hasn’t physically existed in any sense in the world before a month ago, before I invented it, but it sort of intellectually existed forever. There is this abstract world which in some strange sense has existed throughout eternity.
> 
> Imagine an uninhabited planet, full of interesting things. You land on it, and it existed for a million years, but no people have ever been there, no sentient beings. *There are such places, I’m sure. Go to some remote star and there will be something. But you don’t have to go there. You can sit in this very chair and find something that has existed throughout all of eternity and be the first person to explore it.*
> 
> - **John Conway, in "Genius at Play" by Siobhan Roberts**

### Related
- [On Numbers and Games, Conway](https://ollybritton.com/notes/books/on-numbers-and-games/)
- [Winning Ways for your Mathematical Plays](https://ollybritton.com/notes/textbooks/winning-ways-for-your-mathematical-plays/)

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