The citation of this years award is for ``groundbreaking and penetrating work on classical statistical mechanics, integrable models and conformal field theory'' and in this talk I plan to discuss the work in statistical mechanics and integrable models for which the award was given. But since the Heineman prize is explicitly for publications in mathematical physics and since President Clinton has taught us that the proper use of words and definitions is very important I want to begin by examining what may be meant by the phrase ``mathematical physics.''
The first important aspect of the term ``mathematical physics''is that it means something very different from most other kinds of physics. This is seen very vividly by looking at the list of the divisions of the APS. Here you will find 1) astrophysics, 2) atomic physics, 2) condensed matter physics, 3) nuclear physics, and 4) particles and fields but you will not find any division for mathematical physics.
This is very interesting because on the APS web site it further says that ``Each division concentrates on a major specialty within physics... They advance their subfield of physics through nomination of members to Fellowship...and they are represented on the APS Council in proportion to their membership.'' In addition this lack of existence of mathematical physics as a field is reflected in the index of Physical Review Letters where mathematical physics is nowhere to be found.
Therefore we see that the Heineman prize in mathematical physics is an extremely curious award because it honors achievements in a field of physics WHICH THE APS DOES NOT SEEM TO RECOGNIZE AS A FIELD OF PHYSICS.
This lack of existence of mathematical physics as a division in the APS reflects, in my opinion, a deep uneasiness about the relation of physics to mathematics. An uneasiness I have heard echoed hundreds of times in my career in the phrase ``It is very nice work but it is not physics. It is mathematics.' A phrase which is usually used before the phrase ``therefore we cannot hire your candidate in the physics department.''
So the first lesson to be learned is that mathematical physics is an invisible field. If you want to survive in physics you must call yourself something else.
So what can we call the winners of the Heineman prize in mathematical physics if we cannot call them mathematical physicists. The first winner was Murray Gellmann in 1959. He is surely belongs in particles and fields; the 1960 winner Aage Bohr is surely a nuclear physicist; the 1976 winner Stephen Hawking is an astrophysicist. And in fact almost all winners of the prize in mathematical physics can be classed in one of the divisions of the APS without much confusion.
But there are at least two past winners who do not neatly fit into the established categories, Elliot Lieb the 1978 winner and Rodney Baxter the 1987 winner, both of whom have made outstanding contributions to the study of integrable models in classical statistical mechanics--the same exact area for which Wu and I are being honored here today. This field of integrable models in statistical physics is the one field of mathematical physics which does not fit into some one of the existing divisions of the APS.
It is for this reason that I have described integrable models as a hidden field. Indeed it is so hidden that some leading members of the international statistical mechanics community do not even consider it to be statistical mechanics as defined by the IUPAP.
The obscurity of the field of integrable statistical mechanics models explains why there are less than a dozen physics departments in the United States where it is done. This makes the job prospects of a physicist working in this field very slim. But on the other hand it means that we in the field get to keep all the good problems to ourselves. So it is with mixed feelings that I will now proceed to discuss some of the progress made in the last 33 years and the some of the directions for future research.