John Ball is a mathematician whose theoretical work has yielded significant insights into the mechanics of materials. He developed techniques of the calculus of variations in order to show for the first time that the equilibrium equations of nonlinear elasticity for a wide class of materials — including rubber — have solutions. His other contributions include a theory of cavitation in solids and various studies of the approach to equilibrium of physical systems.

His longstanding interest in the structure of matter on microscopic scales has influenced our understanding of phase transitions in solids. John is also a leading researcher in the field of liquid crystals, a unique family of materials whose use in LCD screens has spawned a multibillion-pound industry.

In addition to his scientific work, John has for many years been a leading figure in the international mathematical community, and was one of the founding members of the International Centre for Mathematical Sciences. A former President of the International Mathematical Union, he was knighted in 2006 for services to science.