Richard Ward conducts pioneering and elegant research in mathematical physics. He adapted the twistor transform to the self-dual Yang–Mills (SDYM) equation and, with Michael Atiyah, constructed general multi-instanton solutions. His discovery of the toroidal BPS two-monopole was a breakthrough in soliton theory. He showed that virtually all known integrable equations arise from SDYM by dimensional and algebraic reductions, allowing a unified solution method. Richard’s twistor transform of SDYM, applied to string theory, is leading to striking progress in quantum Yang–Mills theory.