Genius at Play: The Curious Mind of John Horton Conway

I got exactly what I wanted for Christmas this year! This book is great, and I highly recommend it:

True story: One evening in 1996, I remember watching the news with my parents, and the program concluded with a “Persons of the Week” segment, in which the winner of the Westinghouse Science Talent Search was interviewed. Jacob Lurie‘s winning research investigated a certain collection of numbers that, at the time, didn’t seem terribly exciting to me. I asked my parents, “What’s so interesting about serial numbers?” After laughing at my honest confusion, my parents offered some explanation: “He’s talking about surreal numbers, not serial numbers.” But in the absence of wikipedia, no further explanation could be provided.

Almost a decade later, I took advantage of the large math section in my undergraduate school’s library to investigate further. Reading Knuth’s novella (!) on the subject, I learned of a sort of mashup between von Neumann ordinals and Dedekind cuts. I also got the impression that the numbers’ creator — John Conway — was an interesting character. This impression was partially confirmed later when I watched a documentary on Wiles’s proof of Fermat’s Last Theorem, in which John made an appearance: his distinguished-sounding English accent oddly contrasted with his Amish-styled beard and Escher-styled t-shirt. After learning about knots, quaternions, Nim, and Life, it became clear that this interesting character had made quite a broad impact on mathematics.

In the fall of 2009, I arrived at Princeton for my PhD studies, and I made it a mission of sorts to interact with John. I noticed him lounging in the common room scribbling away at something presumably important, so I decided I needed a worthy topic of discussion to warrant imposing myself on him. He had given a series of lectures on the Free Will Theorem in the previous spring, so I watched the first lecture online to prepare for my introduction.

While watching the lecture, I prepared some questions to ask, and then I mustered up the courage to approach John in the common room. To my surprise, he seemed rather interested to talk with me! As Will Sawin later noted, the initial thought one has in this situation is “I can’t believe I’m talking with John Conway!” And then after a couple of hours, one thinks “I can’t believe I’m still talking with John Conway!” Not knowing how talkative John was, I had scheduled a meeting with my research advisor that afternoon, and so I had to be the one to cut “short” our two-hour conversation.

I have fond memories of talking about math and playing games with John throughout my time at Princeton. Perhaps my favorite memory is when I beat John in phutball. While I conveniently forget how much of a handicap he had given me, John forfeited the game after concluding that he couldn’t possibly win, and then Jacob Tsimerman, who had been following the game, interjected with a “no way!” Taking the reins from John, he eventually turned the game around and won!

Boris Alexeev pointed me to this book a month or so ago, and I let my wife know about it (for selfish gifting purposes). Reading this book these last couple of days brought on an intense wave of nostalgia. I had heard many of the stories in this book first-hand, and it’s nice to have them documented for old times’ sake. I also liked how John being an unreliable storyteller forced the biography to be written from the biographer’s perspective. It made the book come alive and kept the pages turning. A few specific comments:

• I remember noticing chalk in the alcove radiators outside the common room, but I always assumed that children had put them there. (not John!)

• I had no idea that John was the source of the bicycle problem. (I was introduced to this problem by Boris, and I love to bring it up in certain company.)

• After John explained the look-and-say sequence to me, he mentioned that people asked him about variants involving Roman numerals and the like. That inspired me to think about the binary version for a couple of hours. (It’s pretty easy to analyze — try for yourself!)

• The best advice he ever gave me also appears in this book: Always keep 4 research problems in mind: A big problem (an open problem like matrix multiplication or deterministic RIP), a workable problem (the sort of problem that puts food on the table like clustering and classification), a book problem (the problems you need to solve to write that book in the future, like various problems in frame theory), and a fun problem (actually, all of these are fun for me).

• I took note that the longest and least interesting chapter of the book was about Life. (While my appraisal is probably biased by my personal lack of interest in Life, the long-winded discussions of various extensions to Life certainly contributed to this chapter’s sluggishness.) To the author’s credit, I thought the length of the chapter did justice to the fact that Life is apparently what John is most known for, and the boringness seems to reflect John’s personal boredom with Life (and his desire for Life to not dominate his legacy).

Again, it’s a great book. Take some time to read it.