He also shed light on the largest of all the sporadic groups, the Monster group, in the “Monstrous Moonshine” conjectures, reported in a paper composed frenetically with his eccentric Cambridge colleague Simon Norton. The biggest of his groups, called the Conway group, is based on the Leech lattice, which represents a dense packing of spheres in 24-dimensional space where each sphere touches 196,560 other spheres. He proved himself by discovering what’s sometimes called Conway’s constellation-three sporadic groups among a family of such groups in the ocean of mathematical symmetry. There’s his first serious love, geometry, and by extension symmetry. Aside from Life, his myriad contributions to the canon run broad and deep, though with such meandering interests he considers himself quite shallow.
Yet when Conway’s vanity strikes, as it often does, and he opens the index of a new mathematics book, casually checking for his name, he gets peeved that more often than not his name is cited only in reference to the Game of Life.
Another purports that when Life went viral in the early-to-mid-1970s, one-quarter of all the world’s computers were playing.Ĭourtesy of James Gardner, Martin Gardner Papers, Special Collections, Stanford University Libraries military report estimated that the workplace hours lost clandestinely watching Life evolve on computer screens cost millions of dollars. The spectacle of Life cells morphing on computer screens proved dangerously addictive for graduate students in math, physics and computer science, as well as for many people with jobs that provided access to idling mainframe computers. Impractically speaking, it became a cult classic for those keen on wasting time. Practically speaking, the game nudged cellular automata and agent-based simulations into use in the complexity sciences, where they model the behavior of everything from ants to traffic to clouds to galaxies. It was coopted by Google for one of its Easter eggs: Type in “Conway’s Game of Life,” and alongside the search results ghostly light-blue cells will appear and gradually overrun the page. Life was among the first cellular automata and remains perhaps the best known. From there Conway, borrowing some Shakespeare, addresses a familiar visitor with his Liverpudlian lilt: With a querying student often at his side, Conway settles either on a cluster of couches in the main room or a window alcove just outside the fray in the hallway, furnished with two armchairs facing a blackboard-a very edifying nook. Inside, the professor-to-undergrad ratio is nearly 1-to-1. The department is housed in the 13-story Fine Hall, the tallest tower in Princeton, with Sprint and AT&T cell towers on the rooftop. Conway can usually be found loitering in the mathematics department’s third-floor common room. By contrast, Conway is rumpled, with an otherworldly mien, somewhere between The Hobbit’s Bilbo Baggins and Gandalf. It’s a milieu where the well-groomed preppy aesthetic never seems passé.
The campus buildings are Gothic and festooned with ivy. The hoity-toity Princeton bubble seems like an incongruously grand home base for someone so gamesome. You can’t put him in a mathematical box.” And the thing about John is he’ll think about anything.… He has a real sense of whimsy. “The word ‘genius’ gets misused an awful lot,” said Persi Diaconis, a mathematician at Stanford University. Yet he is Princeton’s John von Neumann Professor in Applied and Computational Mathematics (now emeritus). Instead, he purports to have frittered away reams and reams of time playing. Based at Princeton University, though he found fame at Cambridge (as a student and professor from 1957 to 1987), Conway, 77, claims never to have worked a day in his life.
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