He earned his PhD at the University of Cambridge, where he later became a professor of mathematics. He became a fellow of the Royal Society in 1981. In 1987, he became the John von Neumann professor of applied and computational mathematics at Princeton University.
He was an eminent mathematician who made important contributions to number theory, game theory, coding theory, group theory, knot theory, topology, algebra, and combinatorics. He invented the Game of Life, a mathematical model of computation.
Son of Agnes Boyce and Cyril Horton Conway.
Youngest of his siblings, with two sisters, named Sylvia and Joan.