The author Siobhan Roberts has sent us a copy of her new book, *Genius at Play*. There was a strong implication that we should review it. I’ve now read the book, so I’ll do that: I enjoyed it.

*Genius at Play* is a biography of John Conway, the mathematician. Look, that’s his face on the cover, surrounded by doodles of some of the maths he’s done.

I first encountered John Conway’s name in the book *Surreal Numbers*, which I found on Amazon back when all it sold was books. (OK, I saw the Game of Life before I saw surreal numbers, but I wasn’t aware of the human being “Conway” who invented it.) That was my introduction to real maths – I was in sixth form at the time and stuck in the world of crank-the-handle algebra – and I suppose it gave me an overly optimistic impression of what grown-up maths might be like. It took me quite a few years after reading maths at uni to rediscover the deliberately unserious strain of maths that Conway champions.

*Genius at Play* is a hybrid biography/autobiography – while Siobhan Roberts is the nominal author, verbatim quotes from Conway are so plentiful and sometimes lengthy that they get their own font, and even that’s not enough – quite often I got the impression that stories covered by Roberts could only have come directly from Conway.

That’s something Roberts clearly grapples with throughout the book – one of the main themes is the unreliability of Conway’s narrative, coupled with the multitude of implausible things that really did happen. When she can, she tries to corroborate facts with other people who were there – a good chunk of the leading mathematicians of our time pop up throughout the book to back up or knock down anecdotes. I’m reminded of the film *Big Fish*, where the line between exaggeration for dramatic effect and implausible reality is distinctly fuzzy.

Going into the book, one of my main concerns was how it would stack up against the other recent popular biographies of great mathematicians. Clearly the publisher thinks that concern will be widely held amongst the readership, as they’ve put a quote from Sylvia Nasar, author of the John Nash biography *A Beautiful Mind*, on the front cover, calling Roberts’ book “Absolutely brilliant”. I can’t really comment on how it compares to the likes of *A Beautiful Mind* or *The Imitation Game*, because I don’t bother reading most books unless the author sends me a copy, but I can agree with that assessment. A significant chunk of the mathematicians interviewed or quoted in this book have had their own biographies written, and at times I began to wonder if Conway was so special after all, when geniuses seem to abound so plentifully. So a Conway biography was definitely overdue.

Going back to films, there have been a significant number of mathematical biopics based on popular biographies recently, so I wondered what the big-budget Hollywood adaptation of this book would be like. Nash, Turing and Hawking all got recast as buff young hunks, so why not Conway? Maybe Michael Sheen could grow a beard to play Conway (is Sheen a buff young hunk? I reckon he bears a decent resemblance to Conway, anyway), and it could be retitled “The Game of Life”. The problem is that *Genius at Play* doesn’t have a big, emotive struggle of the sort faced by Nash and Turing to pin its narrative on – Conway gets his own way more often than a third-act redemption story can support. That didn’t have to be the case, because there are lots of difficult themes that Roberts could have dwelt on: Conway’s suicide attempt is the most dramatic, but there’s also his serial philandering and absolute rejection of all responsibility for his personal affairs. None of that sticks though. The book is written with great affection for Conway, and that seems to be shared by just about everyone interviewed (apart from Stephen Wolfram, who sounds almost like a Bond villain). It comes up again and again that he’s a particularly charismatic man.

Maybe the correct film reference is Willy Wonka. I found myself humming this song on a few occasions:

https://www.youtube.com/watch?v=r2pt2-F2j2g

I’d pay good money to watch Michael Sheen dancing around the halls of the Institute for Advanced Study while singing that.

By the way, “The Game of Life” would’ve been such a perfect title for this book. It’s got everything – the title of the thing everyone knows him for, the book’s about Conway’s life, he treats life as a game. It’s just a shame that Conway really doesn’t want to be “the Life guy”: he says “I HATE LIFE!” with varying levels of sincerity on several occasions throughout the book. That’s understandable: nobody wants to be a one-hit wonder.

It’s good that the book isn’t about John Conway, Inventor of the Game of Life and one-hit wonder, because he’s done enough maths for a twelve-volume *Greatest Hits* collection, with each volume covering a completely different area of inquiry. He’s *The Beatles* to Evariste Galois’ *Ace of Base*, if you will. “Genius at Play” is a good enough title, in the end – what marks Conway apart from his peers is his ideological devotion to playfulness. And there’s no doubt Conway is a genius, by whatever standard.

There’s got to be a lot of maths in a biography of a mathematician, and there’s a lot of it in this book. If it’s going to be a popular book, the maths has to be explained (or abbreviated) in such a way that the general reader can get the gist of it. Consequently, my other main concern going into the book was that the maths would be simplified into incorrectness or so familiar and uninteresting I’d gloss over it. That’s not the case, probably helped in large part by Conway’s more-direct-than-usual input into the text. And frankly, you’d do extremely well to already know all of the maths mentioned in the book. He provides diagrams when necessary, and Roberts lets him take over and explain things when it’s obvious she wouldn’t add anything by paraphrasing him. This engaging style could have been made easier by the common principle in Conway’s work of starting at very simple precepts and finding deep mathematical concepts within while bypassing the intermediate prove-a-ton-of-theorems-and-see-what-sticks step, but even the section about the ATLAS of Finite Groups – definitely not a simple topic – gave me a feeling of understanding what was achieved and a little bit of what it all meant. There are three appendices which go into greater detail about things it’s just not convenient to explain in the main text.

The book starts and ends with a visit to the neuroscientist Sandra Witelson, who wanted to examine Conway’s brain to see if it revealed anything about his genius. I could’ve done without this bit – I went into it sort of disagreeing with the premise, and I wasn’t dissuaded of that. No conclusions were drawn, and I didn’t learn anything new about Conway along the way.

I would’ve liked to see some more thoughtful investigation of Conway’s psychology – the depression and the zany public persona, which are surely linked. There are a couple of allusions to the possibility that Conway’s extroversion is a defence mechanism, but Roberts doesn’t probe too deeply at that, and we’re left to draw our own conclusions. I suppose I just want some opinions spelt out straightforwardly.

Throughout the book, a few different versions of Conway are presented: the conventionally successful mathematician with important theorems and prestigious awards to his name; the scatter-brained eccentric who becomes the subject of urban legends; the charismatic, effervescent trickster god; the irresponsible manchild who exploits those around him; the depressive who worries he hasn’t fulfilled his potential.

Finally, I’ve got a gripe about the typesetting that I need to get off my chest. I don’t know if this is an American thing, but just about every number in the book is printed as a numeral, instead of in words. In a few instances, that’s particularly maddening – when “half of it” was printed as “½ of it”, I winced. It doesn’t really matter though.

*Genius at Play* is a good book, I enjoyed reading it and I learnt a lot.

### More information

*Genius at Play* is published by Bloomsbury, priced \$30 / £20. It’s out now in the US, and from the 10th of September in the UK.

Friend of The Aperiodical Colm Mulcahy is also a friend of John Conway, and he’s written his own review of this book for The Huffington Post. Make sure you read it!

To what is the equation 1969884 = 196883 + 1 a reference? It is just over Conway’s head on the cover.

As to the typesetting of numbers (numerals?), I was raised in the US and taught to spell out numbers ten or less, but use numerals for 11 or greater. You can imagine my English (subject) teacher’s reaction when I asked for clarification of the following cases:

a) 10.5

b) -1,234,567

c) 3.14159

d) sqrt(2)

e) 5 + 2i

In any case, I would generally consider using numerals for small integers to be informal (“there were 2 of us at the table”) but “1/2 of it” is just weird.

It’s a reference to Monstrous Moonshine.

I just thought I’d add this clerihew I wrote on Twitter a few days ago:

My copy refers to “Swiss mathematician Leonhard Fuller” on page 86. Type O behavior?