Last week, life took me through Princeton, and I seized the opportunity to drop in to see resident English mathematician John Horton Conway. He was in particularly good form despite health issues that come with aging, and proudly showed me an advance copy of a forthcoming biography of his life by Siobhan Roberts.

“Being the narcissist I am,” he confessed disarmingly, “I read it in one sitting the day I got it, until 3:30 in the morning.”

John H. Conway holds an advance copy of a forthcoming biography. (Photo: Colm Mulcahy)

We chatted about that fact that this April marks the 40th anniversary of the late mathematics popularizer Martin Gardner's legendary April Fool's column in Scientific American, in which—in the pre-Internet age when it was harder to verify things—Gardner passed off as real six dubious claims that most of his readers swallowed hook, line and sinker. They concerned mathematics, physics, a perpetual motion machine and the alleged invention (by no less than Leonardo da Vinci) of the valve flush toilet.

Over the decades, Conway had inspired several of Gardner's “Mathematical Games” columns, having first corresponded with him in 1957 in response to his breakthrough hexaflexagons article for the magazine. Conway is a rare bird among academics, a consummate showman, being the living embodiment of Gardner's dual philosophy that:

  1. The best way to wake up students to mathematics is via fun activities like games and puzzles (an approach typically avoided by dull teachers)
  2. Exploring the implications and ramifications of "mere brainteasers" can lead to real mathematics of substance.

Conway is a top class mathematician, with few living peers—a totally original thinker who has made deep contributions to areas as diverse as number theory, group theory, game theory, coding theory, geometry and knot theory—while also being the inventor of the “all encompassing” surreal numbers. He has a knack for finding surprising significance in offbeat ideas, and has been a prolific developer of recreational mathematics that bites back, such as the cellular automaton Game of Life, the subject of one of the most famous of all Gardner columns, published in October 1970.

He also has a genius for streamlining discoveries made by others, and coming up with just the right nomenclature, for example, take the case of Penrose tiles. These are now universally explained in terms of “darts” and “kites”, names Conway coined for what he noticed were the essential elemental tiles. Additionally, the iconic cover art for the January 1977 Scientific American column which first introduced Penrose tiles to the public was based on a Conway drawing done at Martin Gardner's house.

The subject of the long-anticipated biography Genius at Play: the Curious Mind of John Horton Conway (Bloomsbury) by Canadian author Siobhan Roberts already has his own early advance copy, but the rest of us will have to await the book’s formal release this summer. Rumor has it that extensive interactions with a host of mathematical luminaries are covered, from Don Knuth, Neil Sloane, Roger Penrose, Steve Wolfram, Richard Guy and Elwyn Berlekamp, to the reclusive American numerologist Irving Joshua Matrix and the French didactic auteur Nicolas Bourbaki.

In the time I spent with him, Conway was happy to chat about the many unusual and talented people he met via his long friendship with Martin Gardner, whom he described in the blurb for Gardner’s memoirs as “the most learned man I have ever met.” He kindly allowed me to videotape some of his musings.

In the following video clip, Conway reveals that it was he who introduced Salvador Dalí to Dr. Matrix (and his beautiful daughter Iva), at a dinner in a restaurant at which Gardner did some startling table magic:

In the next video clip, Conway recalls a stay at Martin Gardner's house, at which he met Nicolas Bourbaki and Benoit Mandelbrot, two famous and very accomplished French mathematicians:

In the third video clip, Conway discusses the dedication of a joint paper by Martin Gardner and Nicolas Bourbaki to Paul Erdős, which had an unforeseen side effect:

In the final video clip, Conway mentions a little-known Gardner/Erdős paper, on a conjecture both deep and profound, written in Kurdish, which he concludes results in Gardner having an Erdős number of 1:

Roberts, whose earlier books include the Euler Prize-winning King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry, admits that the Conway biography took longer than expected to complete, having started it almost eight years ago. “It was challenging and trying at times, working with a live subject, that's for sure!" she remarks. “But on the up-side of that scenario, Conway was game to talk and tell stories ad infinitum—in addition to being a world class mathematician and ambassador-at-large for all sorts of mathy and wordly gems, he's a great storyteller and he truly has a lot of great tales to tell.”

Videos by Colm Mulcahy with post-production by Rob Cook. Thanks to Dana Richards and Derek Smith for creative input.