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Review: ‘Genius at Play: The Curious Mind of John Horton Conway’


Genius At Play: The Curious Mind of John Horton Conway

By Siobhan Roberts


454 pages, $30

By Michael D. Langan

“Genius at Play” sounds like a contradictory title, but it isn’t. “Play” in its broadest intellectual sense is the benevolent mind-host to thousands of good and sometimes worthless ideas.

The key to value is in sorting them out. Claiming to have never worked a day in his life, this is what John Horton Conway does for a living.

Siobhan Roberts is a science writer whose first book, “King of Infinite Space”, (about Donald Coxeter, who “saved geometry”), won the Mathematical Association of America’s Euler Prize for expanding the public’s view of mathematics.

Roberts mentions that writing “Genius” was a collaborative effort. She wanted Conway’s first-person presence to animate the book. That meant that she had to have him sit for countless interviews, and revisit well-worn inquiries. The result was that those interactions formed sufficient permutations to have Conway appear to be speaking for himself in the book.

Some associative background: Remember John Nash, the mathematician, whose life was captured in the 2001 film, “A Beautiful Mind”? His was a mathematical genius. The film caught the elegance, beauty and the personal suffering of Nash, played by Russell Crowe. We observed Nash, who suffered from schizophrenia, succeeding in using his prodigal mathematical gifts while trying fitfully to “fit in.”

“Genius” is the biography of another mathematical genius, John Horton Conway. Conway was educated at Cambridge and taught there, sometimes barefoot, inventing “The Game of Life” in 1970, which involved “exploring the possibilities of simulating human cognition and the potentialities of artificial intelligence.” As Roberts explains, “The emergence of unexpected patterns provides an analogy for evolution.”

As Roberts explains it, Conway was aided and abetted by a loyal following of graduate students in perfecting this game. Conway searched and searched for a simple set of rules, with the goal of producing a universal Turing machine, a computer whose algorithm includes all algorithms.

Conway came to Princeton University in 1986, assuming the title of John Von Neumann Distinguished Professor in Applied and Computational Mathematics. Conway is also a Fellow of the Royal Society of London, the oldest scientific society in the world.

Over the years, he became known as a “campus eccentric with an unconventional lecturing style.” He used cards, ropes, dice, coat hangers and an occasional Slinky as props for learning. He continues as Professor Emeritus of Mathematics at Princeton.

Conway has been awarded many prizes, largely for being a “versatile mathematician who combines a deep combinatorial insight with algebraic virtuosity, particularly in the construction and manipulation of ‘off-beat’ algebraic structures which illuminate a wide variety of problems in completely unexpected ways.”

He has made “distinguished contributions to the theory of finite groups, to the theory of knots, to mathematical logic (both set theory and automata theory) and to the theory of games…” These math specialties will likely mean little to most. Yet we rely on their profundities in practical ways.

Where does Conway work? According to Roberts, “In a spot just outside the fray in the hallway, a window alcove furnished with two armchairs facing a blackboard, with a comfortable amount of legroom in between, Conway does his tinkering.”

In what most would consider a “stretch” of logic, he is working on his latest masterpiece with Princeton colleague Simon Kochen. He calls it the “Free Will Theorem.” The theorem uses quantum mechanics as well as geometry and philosophy to try to prove that if human beings have free will, then elementary particles have free will as well.

How does this follow? Conway conjectures that it goes a long way toward explaining why humans have free will in the first place.

Well, as Touchstone said, “There’s much virtue in an ‘if.’” I don’t see the connection between humans and elementary particles in terms of “free” will, but then again, I’m not Conway.

“Conway’s been in the running for the million-dollar Nobel of mathematics, the Abel Prize – with his group theory work being the strongest point in his favor,” according to Roberts.

Roberts’ book about Conway contains his confession, “I’m confused at various times,” he says, continuing, “In fact, I’m confused at all times. It’s a permanent state.”

If you’re a mathematical genius like Conway, being confused is the beginning of creative thinking.

But Siobhan Roberts is not confused in her explanation of Conway’s gifts. She can elucidate mathematical conundrums for general readers by explaining in nontechnical terms how illuminating confusion can become when Conway probes symmetry groups, plumbs quantum free will, and … develops free insights into how the cosmos evolves … To be sure, free-spirited playfulness has so tangled Conway’s personal life that he once attempted suicide. “But luminous episodes,” Roberts says, “outnumber dark ones in this chronicle of invincible confusion.”

I like the author’s explanation of the man. He’s “Archimedes, Mick Jagger, Salvador Dali and Richard Feynman all rolled into one – a singular mathematician with a rock star’s charisma, a slyly bent sense of humor, a polymath’s promiscuous curiosity, and a compulsion to explain everything about the world to everyone in it.”

Conway puts it this way, “I do have a big ego … As I often say, modesty is my only vice,” he says.

Stanford “mathemagician”– yes, you read that word right – Persi Diaconis, says, “John Conway is a genius. And the thing about John is that he’ll think about anything. Most mathematicians are analysts or group theorists or number theorists or logicians. John has contributed to every single one of those areas, but he doesn’t fit into any.”

I especially like this explanation of his desire to know everything.

“Above all he loves knowledge, and he seeks to know everything about the universe. Conway’s charisma lies in his desire to share his incurable lust for learning, to spread the contagion and the romance. He is dogged and undaunted in explaining the inexplicable, and even when the inexplicable remains so, he leaves his audience elevated, fortified by the failed attempt and feeling somehow in cahoots, privy to the inside dope, satisfied at having flirted with a glimmer of understanding. For his own part, he calls himself a professional nonunderstander. The pursuit is what counts, and chasing after Conway’s promiscuous curiosity and probing his ebullient intellect is this book’s modus operandi.”

Chasing after Conway this way makes this a strange biography. The book is reliant almost entirely on oral history. The reason: Conway keeps no files, no archives, no diaries, no letters, according to Roberts.

Good thing Roberts decided to take him on as a subject using the oral approach. This is especially good for us nonscientists.

“Genius At Play” gives us as much insight into the calculus of Conway’s creative powers as we are capable of capturing with our limited powers.

Michael D. Langan is still puzzling over class notes he took in an infrared spectroscopy course at Canisius College in 1955.