Mathematics and Physics have, over the centuries, had a long and close relationship. The modern era was ushered in by Galileo who said that the laws of nature were written in the language of mathematics. This was taken a giant step forward by Isaac Newton who developed and applied calculus to the study of dynamics. From that time on the whole theoretical framework of physics has been formulated in terms of differential equations.
Both of the 2008 Shaw Laureates in the Mathematical Sciences,Vladimir Arnold and Ludwig Faddeev, are part of this great tradition. Arnold’s contributions are mainly in classical mechanics, emphasizing the geometrical aspects as developed over the centuries by Newton, Riemann and Poincare. Faddeev has been attracted more by the challenges of quantum theory and the algebraic formalism that is related to it.