This is an unusual biography of a highly unusual man, the prodigiously gifted mathematician and professional eccentric John Horton Conway—creative scientist, teacher, showman, and cult figure. His third ex-wife told the author, Siobhan Roberts, that he was both “the most interesting person I have ever met” and “the most selfish, childlike person I have ever met,” and that she didn’t think she would marry again because John had “set the bar rather high.”
Writing about Conway’s work is difficult because it’s all over the map, including significant contributions to number theory, the theories of groups, knots, games, coding, and, more recently, to quantum mechanics. The arc of his story is determined not, as in many scientific lives, by the urge to ever deeper exploration of a few fundamental questions, but by a vow he made, at a critical time, to “stop worrying and feeling guilty” and permit himself to think about whatever pleased him. So, for example, he has devised a clever algorithm for calculating the day of the week on which any given date falls and regularly practices in order to use it as a parlor trick.
“Mathematicians in general don’t do . . . calculational tricks,” he says. “My colleagues in Princeton think it’s rather beneath them. They don’t think anything is beneath me.”
Thus the substance of what Conway does is inseparable from his outsized personality. Roberts, a science journalist, has therefore written an entertaining, often exhilarating, book that reads like a deeply researched magazine profile. (Its website naturally contains a blurb from Conway: “I couldn’t put it down!”) The book consists largely of anecdotes—often very funny, many presumably true—and extensive quotations from a very quotable man: “I have taste but I don’t exercise it very frequently. So I’m just as likely to be doing something that’s not worth doing as something that is.”
Every superhero needs an origin story, and Conway’s comes in two acts. As a schoolboy, he says, he was a shy, insecure outsider, the “math brain.” But when he arrived at Cambridge to begin university studies he realized that, since no one there knew him, he could start from scratch. So he willed himself to become an extrovert. (On first encountering Conway, I wondered: Is he really like that? Is it all an act? The answer, it turns out, is: Yes.)
The curtain went up on Act Two in his early thirties. After a workmanlike Ph.D. he held a teaching appointment at Cambridge but spent most of his time holding court in the mathematics department common room playing backgammon and inventing, other games. He was oppressed by the thought that he had done, and was doing, no work of importance. Enticed by a problem in a then‑hot area—the search for exotic objects called “sporadic groups”—he buckled down and quickly discovered the Conway group.
“Before,” he told Roberts, “everything I touched turned to nothing. Now I was Midas, and everything I touched turned to gold.” Newfound confidence encouraged a life spent following, insouciantly, wherever curiosity might lead.
At the same time, he also became a celebrity to a wider, nonprofessional public by inventing the Game of Life—though he is now dismayed by the possibility that it will be the only thing he’s remembered for. Life was the subject of the most popular article that Martin Gardner ever wrote for his famous Scientific American column, “Mathematical Games.” It is not a game with winners and losers but rather a set of rules for a cellular automaton. Imagine a checkerboard with a limitless number of squares. Mark the board by placing checkers on some of the squares; given any such marking, the rules of Life define the next marking, so that repeated application of the rules causes the board to evolve, step by step.
The rules of Life are simple: Whether a square is occupied in the next position depends on how many of its neighboring squares are occupied in the current one. A checker is removed from a square—having, metaphorically, died of loneliness or overcrowding—if it has too few or too many neighbors, and one is placed on an empty square if a
suitable number of neighbors are available to (metaphorically) procreate there.
Conway’s interest lay in finding simple rules that could produce complex behavior. For example, there is no general procedure for predicting how a marking might evolve (e.g., whether it will eventually die out, leaving an empty board). Some markings act like beings that reproduce by populating the board with copies of themselves; some can simulate fully general programmable computers. The Life craze began before the advent of personal computers, so addicts played by filching millions of dollars’ worth of computer time from their employers.