![]() In Nim, the “board” consists of one or more heaps of counters, and a legal move for a player is to take away as many counters as the player wants from a single pile. I was looking at what are called impartial games, of which the prototypical example is Bouton’s game of Nim. I introduced myself and told him about the work I’d been doing on three-player games. He was (as he would remain throughout his life) happy to have a conversation with a stranger. I found Conway in the Trinity College Common Room one day. Later on, I realized I’d been lucky that Conway wasn’t off taking a sabbatical somewhere (perhaps in the U.S.) during the year I’d left the U.S. When I arrived at Cambridge University, Conway was a Lecturer, not a Professor. It was hard for more traditional academics to know what to make of him. And, unlike most mathematicians, Conway didn’t confine his research to one particular area his breadth of interests would have smacked of dilettantism if he hadn’t made fundamental discoveries in the topics he turned his attention to. Conway’s most profound and distinctive contribution to mathematics, his theory of surreal numbers 3, was shot through with inspirations coming from the study of games, and the achievement he was best known for in the broader world was his invention of a kind of computer-aided solitaire called Conway’s Game of Life. This resolution showed itself clearly in his subsequent output. After he’d discovered three eminently respectable algebraic structures called the Conway groups 2, he’d resolved that from then on he would devote himself to whatever interested him regardless of what other people thought. Perhaps that was partly due to his refusal to draw a line between the serious and the playful the way most mathematicians do. I was awarded a Knox Fellowship, and later that year I went to England on a Knox, as I liked to say (enjoying the resulting homophonic confusion).Ĭonway was a celebrity among mathematicians but hadn’t risen to the top academic rank at Cambridge University. His jest made me worry that I wouldn’t get the fellowship, but he must have believed in me more than his joke suggested. ![]() “You sound a bit like Luke Skywalker heading off to meet Yoda,” the interviewer said. ![]() But I hadn’t even taken the step of writing to the man, and I had to sheepishly admit as much to the interviewer. I’d read about Conway and his multifarious mathematical creations in Martin Gardner’s Mathematical Games column in Scientific American, and I’d become an ardent fan I’d devoured his book “On Numbers and Games” and I’d even done some epigonic 1 work on my own, trying to extend the theory of two-player games to allow for a third player. It was 1982, I was a college senior applying for a fellowship that I hoped would send me to Cambridge University for a year, and the interviewer was voicing justified incredulity at my half-baked plan to collaborate with John Conway. Propp: you plan to go to England to work with a mathematician who doesn’t even know you exist?” ![]()
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