Mathematical physics has made enormous strides over the past few decades, with the emergence of many new disciplines and with revolutionary advances in old disciplines. One of the especially interesting features is the link between developments in mathematical physics and in pure mathematics. Many of the exciting advances in mathematics owe their origin to mathematical physics - superstring theory, for example, has led to remarkable progress in geometry - while very pure mathematics, such as number theory, has found unexpected applications.The beginning of a new millennium is an appropriate time to survey the present state of the field and look forward to likely advances in the future. In this book, leading experts give personal views on their subjects and on the wider field of mathematical physics. The topics covered range widely over the whole field, from quantum field theory to turbulence, from the classical three-body problem to non-equilibrium statistical mechanics.
Modern mathematical physics - what it should be, L.D. Faddeev; new applications of the chiral anomaly, J. Frohlich and B. Pedrini; fluctuations and entropy-driven space-time intermittency in Navier-Stokes fluids, G. Gallavotti; superstrings and the unification of the physical forces, M.B. Green; questions in quantum physics - a personal view, R. Haag; what good are quantum field theory infinites? R. Jackiw; constructive quantum field theory, A. Jaffe; Fourier's law - a challenge to theorists, F. Bonetto et al; the "corpuscular" structure of the spectra of operators describing large systems, R.A. Minlos; vortex-and magneto-dynamics - a topological perspective, H.K. Moffatt; gauge theory - the gentle revolution, L. O'Raifeartiagh; random matrices as paradigm, L. Pastur; wavefunction collapse as a real gravitational effect, R. Penrose; Schrodinger equations in the 21st century, B. Simon; the classical three-body problem - where is abstract mathematics, physical intuition, computational physics most powerful? H.A. Posch and W. Thirring; infinite particle systems and their scaling limits, S.R.S. Varadhan; supersymmetry - a personal view.