Dear President Jackson:

As member of the class of 1966 at the University of Rochester with a dual degree in history and mathematics, I am writing to express my concern about your recent actions, described to alumni as the Rochester Renaissance. This is not a rebirth, it is a Retrenchment. The need to justify your actions to alumni, to the public and to the academic community may be distracting you from a second look at the risk you are taking. You recognize that there will be an immediate and severe loss on the graduate level. But you do not seem to understand that you are damaging the undergraduate program as well.

By now you have heard from Nobel laureates, eminent scientists, distinguished representatives of the professional societies and many dozens of mathematicians and mathematics departments. They are telling you that a research university such as the U. of R. cannot remain outstanding in science without a vibrant and strong mathematics department. They are reminding you that first-rate instruction in mathematics, pure or applied, is not likely to come from temporary teachers, and guaranteed not to emanate magically from machines. They are pointing out that mathematics is central not only to research in science but also to a true liberal arts education. They are telling you this and more, and they are right. Hearing all this again from me can have, at best, a marginal effect. But my experience as a student at the U. of R. and as a professional mathematician is directly relevant to the choice you are making. By telling you about it, I hope to influence you to consider an alternative course.

While I agree with your choice to make selective changes, rather than allow the entire institution to suffer an indiscriminate loss of quality, you seem to have acted solely on the basis of a financial analysis and a questionable competitive ranking (US News and World Report). To remain in some fictional top 30, you seem to be willing to risk losing the special character of the University. Rochester is a small university in a medium-size city with an excellent research science faculty, a great medical school and a strong liberal arts tradition. Comparison makes sense with Washington University in St. Louis, not with Georgetown or MIT. One must have a great mathematics department, the other requires a first-rate history department of a certain sort; Rochester must have both departments of high quality, or else it will lose its special character and wind up competing with Hamilton, not Amherst.^{1}

As an honors-program history major with a strong interest in the sciences, I took graduate courses in mathematics, hung around the math department and got to discuss math with graduate students and young faculty. I also attended many literature courses. In my senior year, I wrote a play, based on a short story by a dissident Soviet author, and helped produce it on campus. The production included rear-projection film sequences that we made with equipment loaned from Eastman Kodak. I went on to spend a year at Princeton in the graduate program in the history of science, and from there I went to Stanford where I wrote a Ph.D. in mathematics. At the University of Massachusetts, where I was on the faculty of mathematics for twenty years, I cofounded the Center for Geometry Analysis Numerics and Graphics. This laboratory supported productive research interactions between mathematicians, graphics programmers, networking specialists, physicists, chemists, chemical engineers and polymer physicists. We aided in various ways the work of geo-scientists, landscape architects, forest conservationists and educators at all levels. There was frequent and productive interaction between senior faculty, post-docs, graduate students, undergraduates and (yes) the occasional high-school student. In one area of geometry, we pioneered the use computer graphics and animation in pure research. The use of graphics allowed us to communicate with material scientists and to collaborate with them in developing new models that were not only theoretically justifiable from a mathematical point of view, but were also testable by laboratory software (jointly developed) which compares these models to laboratory experiments. I have help create several widely-traveled museum exhibitions about mathematics and its applications. These are organized around the computer-graphics images and animation produced in the research that I have done with others. Currently, I am Head of the Scientific Graphics Initiative at the Mathematical Sciences Research Institute in Berkeley, California. Here, in the past month, I have discussed specific scientific problems with researchers in human vision, computational quantum chemistry and polymer physics; all of them involved non-trivial theoretical mathematics.

At Rochester, I was exposed to a great deal of science, first-hand, in an atmosphere that highly valued the humanities and the arts. It is evident to me and I hope it is clear to you that this has been a strong influence on my career. For me, all these things came together around mathematics. Without a strong graduate program in mathematics, I could not possibly have had this formative undergraduate experience. Such an experience will be impossible after the Rochester Retrenchment. Replacing mathematics professors by part-time and temporary workers will lower the quality of instruction at the entry level. A ``teaching specialist'' in calculus could never have given me the insight, challenges and encouragement I got from professional research mathematicians at the U. of R., even those who were not great classroom instructors. Terminating the graduate program without some balancing moves will make it impossible for undergraduate majors in mathematics, computer science or history to take graduate courses in mathematics and to participate in a real mathematical life.

One of your stated goals is to make the U. of R. a premiere undergraduate institution, on a par with Amherst or Williams. The University of Massachusetts, Amherst, is five minutes by bus from Amherst College. Professors at Amherst can and do teach courses at UMASS, and vice verse. Many students from Amherst College take graduate courses at UMASS. The Five College System, which includes UMASS and Amherst, supports a number of seminars and programs in mathematics (as well as other areas of the sciences and humanities) which are open to undergraduate participation. I was a coauthor of the first NSF Grant for one of them, the Valley Geometry Seminar, which still thrives. Because of this, Amherst College can attract faculty with strong research interests and they can teach and mentor graduate students. Amherst college students can and do take graduate courses in mathematics at UMASS. Amherst does not use part-time faculty to teach their courses as you are planning to do. Their students are exposed to a research environment. Termination of the graduate program in mathematics will prevent you from attracting the type of student who goes to Amherst College.

Williams College is a good hour away from Amherst, but there is still a good deal of interaction and I can offer you some more information that will give you a better view of what is going on there. The mathematics program languished there for a good many years until they sought out and hired Frank Morgan, a serious research mathematician who is also an equally serious undergraduate educator, possessed of boundless energy. Coming from MIT, where he was largely in charge of the calculus program, among other things, Morgan instituted now-famous research seminars for undergraduates and secured funding for these seminars and for high-quality visitors to Williamstown. Given the fact that you do not plan to hire any mathematician in the foreseeable future and that you can expect your most capable mathematicians to leave, there is simply no way you will be able to match Williams in this regard.

Mathematics as a subject and a profession is in a period of enormous change, the most profound in the last two hundred years. (As someone with a life-long interest in the theater, stemming from my undergraduate days at Rochester, let me suggest you see or read ``Arcadia,'' by Tom Stoppard, for another view of the how mathematics is changing but remaining central to human thought.) This is due in part to the advent of modern computing machines that are, as a friend once put it, the first new laboratory instrument for mathematicians since the invention of the method of proof in Antiquity. The ability to compute symbolically and to simulate numerically has had the paradoxical effect of making theoretical understanding more important, not less so. The vastly increased speed at which mathematical ideas find use in scientific disciplines, and then bounce back to mathematics in new forms--wavelet theory is one example, modern cryptography schemes another--has accelerated the tempo and expanded the scope of mathematics. It is no wonder that there is some confusion about what should be at the core of the mathematics curriculum and much controversy about how it should be taught. These are signs of change in a period of transition; they are not indications of irrelevance or decay. Mathematics is becoming more, not less, important in the sciences and in engineering.

Rochester needs a first-class mathematics department with graduate research involvement. Perhaps the current department should be differently configured, but it should not be decapitated. I suggest that you give the mathematics department a choice similar to the one you gave to the history department: conversion of graduate lines to a smaller number of post-doctoral positions. Three-year post docs could be hired with research interests that either are compatible with those of the faculty, or lie at the intersection of mathematics and one of the strong sciences on the River Campus. They should have teaching responsibilities and the charge to have a great deal of contact with undergraduates. Research faculty could act as mentors and collaborators. At the same time, exposure to the high-quality science on the Campus and to Rochester's industies that requires highly trained scientists will allow some of them to redirect their careers, if necessary. The graduate program could be curtailed but not terminated. Why refuse to let a really good student do a Ph.D. with a world-class faculty member in the active mathematical environment I am proposing? Just set the bar very high.

This is one alternative and there surely are others. Do not mistake your dissatisfaction with the mathematics department you have--based on ratings or grant income, or some other unstated friction with current department members--for a rationale to have a weak mathematics program. You have everyone's attention and your actions are being watched worldwide. The University's reputation really is at stake here. You do have the right to demand more, but you cannot solve the problem by removing serious mathematics. Please reconsider and make a constructive change, not the swift, destructive cut from which it will take twenty years to recover.

David Hoffman

Mathematical Sciences Research Institute

1000 Centennial Drive

Berkeley CA 94720