10/13/2004

Weinen E
Princeton University

Crisis in applied mathematics

For more than fifty years, applied mathematics has enjoyed tremendous success in many areas of physical science and engineering, most notably fluid mechanics and structural mechanics, in which macroscopic models in the form of PDEs play the major role. In contrast, it has paid relatively little attention to areas such as computational chemistry and molecular biology where the models tend to be more discrete and the physics tends to be more microscopic. In recent years, it has become increasingly clear that this lack of involvement in discrete models and microscopic physics is becoming a major obstacle to the further development of applied math. The recent explosive growth of interest on multiscale, multi-physics  modeling from other scientific disciplines has made this a rather urgent issue to be dealt with. In this talk we will analyze the background ofthis problem and discuss possible solutions, particularly in the form of a new curriculum. We will also discuss the new challenges that will arise in mathematics from this change of style in applied math.