Book Review: "Genius at Play" by Siobhan Roberts

I've recently been able to read the book Genius at Play by Siobhan Roberts. It is a biography of John Conway from his high school days onward, covering a lot of his work on group theory, symmetries, number theory, and other fields; it does discuss the Game of Life but goes deeper into drawing out the evolution of his response to being solely associated with it, from joy to despair to resigned ambivalence. It also goes through various episodes in his personal life, and frequently switches between narrating recollections of past events and narrating the current events surrounding those recollections themselves. It shows what a whimsical, joyful, carefree, and gregarious man he has been when it comes to math, but while much of the middle section of the book makes this seem like his core personality, the beginning parts about him reinventing his personality after high school, the middle parts about others' (particularly Stephen Wolfram's) characterizations of him, and the end parts about his own feelings about it now (as an older man) make clear that the carefree part of his nature has been more of a facade to cope with his own ego & attendant insecurities.

I really enjoyed this book's progression through his life. It allowed me to once again experience the joys of seeing seemingly inconsequential math ideas that are easy to introduce but hard to truly explain to broad lay audiences, like I did in middle school with my fascination with numbers like pi and the golden ratio and the really random places they pop up. Plus, that juvenile whimsy combined with the human interest in reading about John Conway as a person, as well as my more mature recent interest in deeper philosophical questions, like the physical reality of mathematical theorems (whether they are invented by humans or discovered from the course of nature), or the nature of free will at the human versus subatomic quantum scales. The writing of this book really seemed reflective of John Conway's whimsical and sometimes scattered personality as well as of the people and environment surrounding him, painting a vivid picture of the man in context; I appreciated this to the same extent that I did Robert Kanigel doing the same for Ramanujan in The Man Who Knew Infinity, though in the latter case, Ramanujan seemed to be a rather shy person for whom information had to be gleaned from other sources (also because Kanigel wrote that biography many decades after Ramanujan's death), so Kanigel successfully painted the picture of the people and environment in India and the UK that shaped Ramanujan's personality and the course of his life. Overall, this was a really enjoyable book that went by quickly despite its length. Perhaps people who are slightly more acquainted with the basics of higher-level mathematics may enjoy it more than laypeople (and I would probably enjoy it more if I knew more math); nevertheless, I think the storytelling is quite engaging and accessible to a broad audience. Follow the jump to see a couple other brief thoughts.

The only issue I had was with Conway's distinction of free will, determinism, and randomness, because in his microscopic framework of free will, not only is free will itself somewhat ill-defined, but the notion of randomness also seems to be poorly defined beyond existing in the past, so it isn't clear whether true randomness is definable in this framework of free will, whether in a frequentist, Bayesian, or other sense. That said, this has more to do with Conway's own work rather than the book per se. Plus, I am neither a philosopher nor a probability theorist, so I don't really have the tools to comfortably delve further into this issue in a public space like this blog.

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