Pick up Genius at Play: The Curious Mind of John Horton Conway by Siobhan Roberts and chances are you won’t be able to put it down. Just out, the book already has a waiting list at the Princeton Public Library.

Its subject is the Princeton University mathematician, or “mathemagician” as he’s been called, who invented the cult classic Game of Life back in the 70s. The game, known simply as Life, demonstrates how complexity can come from simplicity, providing an analogy for all mathematics and everything in the entire universe.

Born in Liverpool in 1937, Mr. Conway found fame as a barefoot Cambridge professor. He discovered the Conway groups in mathematical symmetry and invented the aptly named surreal numbers. He has been known to recite π from memory to 1,111 digits. And he came to Princeton in 1987 to become the John von Neumann Professor at the University.

Like von Neumann, Mr. Conway is a polymath; his contributions to game theory, knot theory, number theory, coding theory, group theory, and geometry are legendary. With good reason he is a Fellow of the Royal Society, along with his Cambridge colleague Stephen Hawking and such past luminaries as Alan Turing, Albert Einstein, Bertrand Russell, and Isaac Newton.

As revealed in Genius at Play, he is an endearing individual of insatiable curiosity. Ms. Roberts had full access to her subject, whom she investigates with gusto, exploring both professional and personal idiosyncrasies.

The Toronto-based Canadian journalist and science writer has won no less than four National Magazine Awards and her first book, King of Infinite Space: Donald Coxeter, the Man who Saved Geometry, won the Mathematical Association of America’s Euler Prize. She came to Genius at Play while researching for that book. Coxeter, it turned out, was a hero of Mr. Conway’s, and the biographer interviewed him at a summer mathematics camp. “Witnessing him playing endless games with kids, it became abundantly clear that this was his natural milieu; there was no other way he’d rather spend his time.”

Mr. Conway read Ms. Roberts’s manuscript and ended up talking about himself: “about crashing overnight at the Kremlin in ’66, about attending the burial of Cromwell’s skull at Cambridge, about his three wives and all the other women, more than he can count (he tried once during a bout of insomnia) …. He’s a talker, not a listener. While Coxeter epitomized the reticent and restrained Edwardian gentleman, Conway is the rare man inclined to forthright and global disclosure.” The biographer had discovered her next subject.

While writing Genius at Play, Ms. Roberts spent time at the Institute for Advanced Study as a Director’s Visitor at the invitation of then IAS Director Peter Goddard.

A biographer has a daunting enough task when her subject is dead, but when her subject is very much alive, that task is doubly challenging. How does Ms. Roberts cope with her larger than life subject? She does it in a novel way that features the mathematician’s comments, anecdotes, reminiscences and discursive digressions throughout the book, set off in a distinct typeface. She allows the masterful storyteller room to spin yarn. “Writing the book was a decidedly collaborative effort,” she said. “Conway sat for countless interviews, willingly (and sometimes unwillingly).”

According to popular science writer Martin Gardner, “Conway is a creative genius.” Genius at Play describes him as “an unabashed original: Archimedes, Mick Jagger, Salvador Dali, and Richard Feynman all rolled into one with a “slyly bent sense of humor” and “a compulsion to explain everything about the world to everyone in it.”

The book has received rave reviews from the likes of Sylvia Nasar, author of A Beautiful Mind and Grand Pursuit; James Gleick, author of The Information and Chaos; and Roger Penrose, author of The Road to Reality and The Emperor’s New Mind.

Read Genius at Play “if you want to know what it feels like to be with Conway,” said Columbia University mathematician Michael Harris in his 23 July Nature review of Mr. Roberts’s book. “Roberts breathes more life into the stories of a living mathematician than I thought possible. [Her] ‘kaleidoscope of inquiry’ is a marvel for its virtuoso juggling of narrative speeds, reminiscences, implausible digressions, and long passages of precise, comprehensible mathematics. She packs it all into a tidy chronology framed by the story of a road movie starring Conway; she plays his amanuensis, occasional driver and ‘back channel’ through which the world communicates with this most mercurial and untidy of mathematicians,” wrote Harris.

And the best part is, you don’t need a PhD in mathematics to enjoy this book. For more information on Genius at Play (ISBN 978-1-62040-593-2), visit: www.bloomsbury.com.