John Horton Conway is a great mathematician, certainly one of the greatest living mathematicians. Polymathematical in his mathematical interests (game theory, geometry, group theory, topology and more, not to mention the Game of Life), he's also one of the most eccentric, and that's saying a lot in a field where Cedric Villani is prime eccentricity competition.

As one can imagine, the biographer of an oddball character like Conway faces certain ... challenges ... that most biographers don't face. Memory, obstinacy, whimsy, the whole nine yards.

So it pleases me to say that Siobhan Roberts' recent biography, Genius At Play The Curious Mind of John Horton Conway, rises to the occasion and gives a wonderful and quirky portrayal of a wonderful and quirky figure in the history of mathematics.

But it must be said. If the author of a book about such an unconventional

unusual, irregular, unorthodox, unfamiliar, uncommon, unwonted, out of the ordinary, atypical, singular, alternative, different; new, novel, innovative, groundbreaking, pioneering, original, unprecedented; eccentric, idiosyncratic, quirky, odd, strange, bizarre, weird, outlandish, curious; abnormal, anomalous, aberrant, extraordinary; nonconformist, Bohemian, avant-garde; informalfar out, offbeat, off the wall, wacky, madcap, oddball, zany, hippie, kooky, wacko (here)

figure faces some challenges, so does the reviewer of such a book. How to convey both the book subject's personality and how that personality is reflected in the book itself? Because make no mistake, Roberts does a great job of mirroring Conway's personality

the combination of characteristics or qualities that form an individual's distinctive character.

"she had a sunny personality that was very engaging"

synonyms: character, nature, disposition, temperament, makeup, persona, psyche

"her cheerful personality"

qualities that make someone interesting or popular.

"she's always had loads of personality"

synonyms: charisma, magnetism, strength/force of personality, character, charm, presence

"she had loads of personality" (here)

in the way she tells the story -- fresh, fun, whimsical, a bit wild and offbeat. But not purposefully difficult or obtuse or overly wilful or inventively fanciful with details (like Conway also can be), I guess leaving those aspects out of the direct telling of the tales.

What I'm going to do is leave it to the book itself to tell it's own tale. Here's a bunch of quotes, I won't tell you who from, from Roberts or Conway or one of the other people quoted in the book. 'Cause where would the fun be in that.

- p. 20: There goes somebody looking strange. Ergo it must [be] a friend of Dad's!
- p. 25: You know, it's hard to think what message to send your tongue to get it to do this thing.
- p. 51: I'm a Platonist at heart, although I know there are very great difficulties with that view.
- p. 57: Mercifully, the hiring process for the Cambridge mathematics faculty was then loosey-goosey, somewhere between anarchic and irrational.
- p. 64: "Had the baby?" / Yes. / "Boy or girl?" / Yes.
- p. 74: Were my lectures anywhere near that coherent?
- p. 75: The smitten students loved him as much for his mind as his silly high jinks, and maybe most of all for his singular hybrid of sophistication, sincerity, and lascivious showmanship.
- p. 82: Cue the tremolo whistle that presage a duel in "The Good, The Bad, and the Ugly." It's a mathematicians shootout. Who's the fastest to draw to draw a stellated icosahedron.
- p. 97: During a trip to Montreal there was 8 inches of snow. Conway, as per usual, was wearing only his sandals.
- p. 107: Are there any determinists present?
- p. 124: I like to think of a huge abandoned warehouse equipped with logical devices such as AND, OR, and NOT gates.
- p. 128: It terrifies him that another of his worst nightmares might come true, that his life will in the end be reduced to Life.
- p. 133: You know, when you play a game, if you learn to be good at it, you find what it is you should be thinking about. That is really rather subtle. And that's what we do in mathematics.
- p. 139: Come again? (As the actress said to the bishop.)
- p. 145: Which is to say, Life could calculate pi. It could calculate anything. In the broadest logical sense, Life was a metaphor for all of mathematics; it contained all of mathematics.
- p. 181: No. Yes. I'm not sure, to tell you the truth.
- p. 186: Conway carries the Shannon philosophy to its extreme, often forced by his lack of system to rediscover his own results.
- p. 213: Suppose surreal numbers had been invented first and real numbers second -- suppose it had gone the other way and we had all grown up learning surreal numbers.
- p. 224: Conway's philosophy of study, which has served him well, is to always take his investigations several steps beyond what any reasonable human being would do.
- p. 224: No no no no no! You're being far too REASONABLE.
- p. 237: I arrived at the alcove armed with the "Monstrous Moonshine" paper...in hopes of getting, if not an answer, at least some elaboration about what exactly he and Norton had accomplished.
- p. 242: Conway employs an entomologically inspired algorithm in explaining his own mating patterns.
- p. 244: How, pray tell, does an unkempt nerdy mathematician get so lucky?
- p. 275: It's one of the surest signs of senility in a scientist -- or a mathematician, for that matter -- when after having made a reputation in one subject, he somehow feels he can make a contribution to something else.
- p. 364: We are parasites, we mathematicians, on the proper function of the brain.
- p. 379: But my view is we are trying to find the truth, and there are other ways of finding the truth than proofs. And this is unsettling to mathematicians.
- p. 390: Gareth, it must be said, is as psyched about having a nerd for a father as any boy could be.

You get the idea. And you'll have to get a hold of the book itself to figure out the context of the odder of the quotes above. Parasites. *snort*

Needless to say, this is an excellent book, one that belongs in every library's mathematics collection, academic or public. It is also indispensable for collections in the history of science or math. It would also make an excellent addition to the personal collection of any lover of math or personality.

(Review copy provided by publisher.)

Roberts, Siobhan. Genius At Play: The Curious Mind of John Horton Conway. New York: Bloomsbury, 2015. 480pp. ISBN-13: 978-1620405932

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