Siobhan Roberts in The Guardian:
For the last quarter century Conway has held the position of Princeton’s John von Neumann distinguished professor in applied and computational mathematics, now emeritus. Before that, he spent three decades at Cambridge, where in the 1970s, he dived deep into the vast ocean of mathematical symmetry. He discovered a 24-dimensional symmetry group that came to bear his name, and, with his colleague Simon Norton, he illuminated the 196,883-dimensional Monster group with a paper titled “Monstrous Moonshine”. Conway also discovered a new class of numbers, infinitely large and infinitesimally small, which are now known as “surreal numbers”. Those achievements earned him a spot as a fellow of the Royal Society of London for Improving Natural Knowledge, the oldest scientific society in the world. Conway likes to mention that when he was elected in 1981, he signed the big book of fellows at the induction ceremony and was pleased to see on previous pages the names Isaac Newton, Albert Einstein, Alan Turing, and Bertrand Russell.
Conway’s is a jocund and playful egomania, sweetened by self-deprecating charm. He has on many occasions admitted: “I do have a big ego! As I often say, modesty is my only vice. If I weren’t so modest, I’d be perfect.” That said, he is irresistibly drawn to piddling away his days playing games, preferably silly children’s games.