Maynard Smith was educated at Cambridge University, where he qualified as an engineer in 1941. He spent the next six years designing aircraft before deciding they were “noisy and old-fashioned” and moving to University College, London, to study zoology under J. B. S. Haldane. After obtaining his BSc in zoology in 1951 he remained as a lecturer in zoology until 1965 when he was appointed professor of biology at the University of Sussex. He became emeritus professor in 1985.

Maynard Smith, known to a wide public for his lucid Theory of Evolution (1958), has emerged as one of the leading theorists of the postwar years. Much influenced by W. D. Hamilton and Robert MacArthur, and using concepts taken from the theory of games formulated by John von Neumann in the 1940s, he introduced in the 1970s the idea of an evolutionary stable strategy (ESS).

Assuming that two animals are in conflict, then an ESS is one that, if adopted by the majority of the population, prevents the invasion of a mutant strategy. Stable strategies by definition thus tend to be mixed strategies.

Much of Maynard Smith's work on ESS was published in his Mathematical Ideas in Biology (1968). He also discussed why sexual modes of reproduction predominate over other means in The Evolution of Sex (1978). Maynard Smith has continued to write on evolutionary theory in such works as Evolutionary Genetics (1989) and The Major Transitions of Evolution (1995).