The 1999 Heineman Prize Address Integrable Models in Statistical Mechanics: the Hidden Eld with Unsolved Problems

In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear diierential equations for Ising model correlation functions, the theory of random impurities, level crossing transitions in the chiral Potts model and the use of Rogers-Ramanujan identities to generalize our concepts of Bose/Fermi statistics. Each of these advances has led to the further discovery of major unsolved problems of great mathematical and physical interest. I will here discuss the mathematical advances, the physical insights and extraordinary lack of visibility of this eld of physics.