Strauss received a Ph.D. in Mathematics from M.I.T. in 1962. After an N.S.F. postdoctoral fellowship at the University of Paris and three years at Stanford University, he joined the Department of Mathematics at Brown in 1966 and subsequently the Division of Applied Mathematics. He chaired the Department of Mathematics during the periods 1989-92 and 2000-2001. He has received Fulbright and Guggenheim Fellowships and an Institut Henri Poincare Prize and he is a Fellow of the Society of Industrial and Applied Mathematics. He has visited, for a semester or more, each of the following: C.U.N.Y., U. of Paris, U. of Tokyo, M.I.T., U. of Maryland, Yunnan U., Courant Institute (NYU), U. of Houston, Inst. H. Poincare (Paris), Duke U. and the Mittag-Leffler Institute (Sweden). He was the Editor-in-Chief of the SIAM Journal on Mathematical Analysis during 2000-2007.
Strauss is the author of more than 100 research articles and two books. The main focus of his research has been the analysis of nonlinear waves. They are modeled by hyperbolic, elliptic or dispersive partial differential equations. Some of his specific research areas have been scattering theory in electromagnetism and acoustics, stability of waves, relativistic Yang-Mills theory, kinetic theory of plasmas, theory of fluids, and water waves.