in 2011 he succeeded sir david wallace as director of the isaac newton institute for mathematical sciences and n m rothschild & sons professor of mathematical sciences at the university of cambridge. in 2016 he was succeeded as director by professor david abrahams. his research interests include mathematical analysis and nonlinear partial differential equations with particular interest in the rigorous theory of steady water waves. in 1978, he proved george gabriel stokes' conjecture on the existence of gravity waves of maximum height on deep water, a previously open problem in mathematical hydrodynamics which dated back to the 19th century.