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Why is a research mathematics program necessary for graduate science programs?

Stephen Weinberg, Nobel Laureate in Physics, in a letter to the president of the University of Rochester regarding their decision to cut back the math program:

"I am not a mathematician, but I regard mathematics as the core of any research program in the physical sciences. My own work as a theoretical physicist (which was honored in 1979 with a Nobel Prize) has been enriched by contacts with active researchers in mathematics at all the universities at which I have worked: Columbia, Berkeley, M.I.T., and Harvard as well as Texas. If you do not have a graduate program in mathematics then eventually you will have no research mathematicians, which will make Rochester far less attractive to theoretical physicists. Experimental physicists may not feel the loss of the mathematics program directly, but with with fewer first-rate theoretical physicists you will begin to lose your best experimentalists as well. You will also be weakened in your ability to compete for good students; both graduate and advanced undergraduate physics students need to take advanced courses in mathematics, which can only be taught well by active research mathematicians. I imagine that similar effects will eventually be felt in your chemistry and optics departments. I would not advise any prospective undergraduate or graduate student who wishes to concentrate on the physical sciences to go to a university that did not have a graduate program in mathematics.

I do not know the details of Rochester's financial problems, but I do understand that you may find it necessary to cancel some of your graduate programs. Nevertheless, it seems to me extremely unwise to eliminate your program in an area like mathematics, that stands at the intellectual center of a large part of modern science."

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