Short Summaries of Articles about Mathematics
in the Popular Press
"How to melt if you must," by Ivar Ekeland. Nature, 16 April 1998.
Partial differential equations are the primary tool used by physicists to model physical behavior, from the dissemination of heat through water to the orbits of the planets. Unfortunately, not all partial differential equations can be solved by known mathematical techniques. This article describes the recent proof of a conjecture by Ennio de Giorgi which relates to the solution of a possible nonlinear partial differential equation model for melting ice. In addition to proving a single solution to the model, it was shown that this solution behaves very differently depending on the dimension of the problem.