John Horton Conway (1937-2020)

While it hasn’t yet been officially confirmed, the news has spread across social media (see e.g. here, here, here) that John Horton Conway, one of the great mathematicians and math communicators of the past half-century, has died at age 82.

Just a week ago, as part of her quarantine homeschooling, I introduced my seven-year-old daughter Lily to the famous Conway’s Game of Life. Compared to the other stuff we’ve been doing, like fractions and right triangles and the distributive property of multiplication, the Game of Life was a huge hit: Lily spent a full hour glued to the screen, watching the patterns evolve, trying to guess when they’d finally die out. So this first-grader knew who John Conway, was when I told her the sad news of his passing.

“Did he die from the coronavirus?” Lily immediately asked.

“I doubt it, but I’ll check,” I said.

Apparently it was the coronavirus. Yes, the self-replicating snippet of math that’s now terrorizing the whole human race, in part because those in power couldn’t or wouldn’t understand exponential growth. Conway is perhaps this nasty bugger’s most distinguished casualty so far.

I regrettably never knew Conway, although I did attend a few of his wildly popular and entertaining lectures. His The Book of Numbers (coauthored with Richard Guy, who himself recently passed away at age 103) made a huge impression on me as a teenager. I worked through every page, gasping at gems like eπ√163 (“no, you can’t be serious…”), embarrassed to be learning so much from a “fun, popular” book but grateful that my ignorance of such basic matters was finally being remedied.

A little like Pascal with his triangle or Möbius with his strip, Conway was fated to become best-known to the public not for his “deepest” ideas but for his most accessible—although for Conway, a principal puzzle-supplier to Martin Gardner for decades, the boundary between the serious and the recreational may have been more blurred than for any other contemporary mathematician. Conway invented the surreal number system, discovered three of the 26 sporadic simple groups, was instrumental in the discovery of monstrous moonshine, and did many other things that bloggers more qualified than I will explain in the coming days.

Closest to my wheelhouse, Conway together with Simon Kochen waded into the foundations of quantum mechanics in 2006, with their “Free Will Theorem”—a result Conway liked to summarize provocatively as “if human experimenters have free will, then so do the elementary particles they measure.” I confess that I wasn’t a fan at the time—partly because Conway and Kochen’s theorem was really about “freshly-generated randomness,” rather than free will in any sense related to agency, but also partly because I’d already known the conceptual point at issue, but had considered it folklore (see, e.g., my 2002 review of Stephen Wolfram’s A New Kind of Science). Over time, though, the “Free Will Theorem” packaging grew on me. Much like with the No-Cloning Theorem and other simple enormities, sometimes it’s worth taking a bit of folklore and giving it a clear name and referent.

At a lecture of Conway’s that I attended, someone challenged him that his proposed classification of knots worked only in special cases. “Oh, of course, this only classifies 0% of knots—but 0% is a start!” he immediately replied, to roars from the audience. That’s just one line that I remember, but nearly everything out of his mouth was of a similar flavor. I noted that part of it was in the delivery.

As a mathematical jokester and puzzler who could delight and educate anyone from a Fields Medalist to a first-grader, Conway had no equal. For no one else I can think of, possibly in all of history, were entertainment and mathematical depth so closely marbled together. Here’s to a well-lived Life.

Feel free to share your own Conway memories in the comments.