Arthur studied at Princeton and Cambridge Universities, starting in experimental chemistry, transitioning through mathematics, and ending in theoretial physics. He established the compatibility of special relativity with quantum theory, by demonstrating the existence of non-linear quantum field theories in space-times of dimension two and three. (This problem in dimension four is still unresolved.) He has been on the faculty of Harvard University since 1967, and served as President of the International Association of Mathematical Physics, President of the American Mathematical Society, Chair of the Council of Scientific Socity Presidents, and in other positions. He was a founding member, director, and first president of the Clay Mathematics Institute, popularly known for offering a seven million dollar prize for the solution of seven mathematical questions.