Dr. Conway’s mother, a great reader, especially of Dickens, had worked from age 11. Family lore has it that she boasted about finding her son at age of 4 reciting the powers of two. At 18, in 1956, John left home for the University of Cambridge, where he earned his Ph.D. His adviser, Harold Davenport, a number theorist, once said that when he would give Dr. Conway a problem to solve, “he would return with a very good solution to another problem.”
As a student, Dr. Conway cultivated his acknowledged lifelong preference for being lazy, playing games and doing no work. He could be easily distracted by what he called “nerdish delights.” He once went on a flexagon binge, courtesy of Mr. Gardner, who described flexagons as “polygons, folded from straight or crooked strips of paper, which have the fascinating property of changing their faces when they are flexed.”
He built a water-powered computer, which he called Winnie (Water Initiated Nonchalantly Numerical Integrating Engine). He read and annotated H.S.M. Coxeter’s edition of W.W. Rouse Ball’s classic work, “Mathematical Recreations and Essays” and wrote Coxeter a lengthy letter that started a lifelong friendship between these two classical geometers.
Hired at Cambridge as an assistant lecturer, Dr. Conway gained a reputation for his high jinks (not to mention his disheveled appearance). Lecturing on symmetry and the Platonic solids, he might bring in a turnip as a prop, carving it one slice at a time into, say, an icosahedron, with its 20 triangular faces, eating the scraps as he went. “He was by far the most charismatic lecturer in the faculty,” his Cambridge colleague Peter Swinnerton-Dyer once said.
Dr. Conway invented a profusion of games — like Phutball (short for Philosopher’s Football, which is a little like checkers on a Go board) and collected them in the book “Winning Ways for Your Mathematical Plays,” in collaboration with Elywn Berlekamp and Richard Guy.
All the gaming was supported by a loyal following of graduate students, among them Simon Norton, with whom Dr. Conway published the Monstrous Moonshine conjecture, investigating an elusive symmetry group that lives in 196,883 dimensions. (His Ph.D. student Richard Borcherds received the prestigious Fields Medal in 1998 for his proof of the conjecture.)