Duncan A. Buell is member of the research staff at the Center for Computing Sciences (CCS), Institute for Defense Analyses (IDA), located in Bowie, Maryland. The business of IDA is research in mathematics and computation in support of the mission of their sponsor, the National Security Agency (NSA). The mission of the NSA, a government agency, is to protect U.S. communications and to produce foreign intelligence information. The CCS is made up of 45 research staff, mostly Ph. D. holders. The backgrounds of the research staff are about equally divided among a) traditional mathematics, b) computer science, c) electrical engineering, and d) an "other" category that includes other engineering disciplines, the computational side of the hard sciences, and applied computational math/operations research.
"My role at IDA is research in its broadest sense," says Duncan. "I've done some pure research both on my own and with other people, both classified and unclassified. For nearly three years I led a project to build a novel computer that (in a re-engineered and "productized" form) is now available for sale by a private company. And I've done some research on some very specific problems that came from NSA, this mostly as part of a larger team."
"I personally don't know from one day to the next whether I should be thinking of myself as a computer scientist or a mathematician," he continues. "I'm not usually a pure mathematician. On the other hand, what I am doing is working through solutions, usually computational ones, to problems that are inherently mathematical. Either way, the basic problems in NSA's business--cryptography--are fundamentally mathematical. NSA's problems in mathematics and computing are probably the biggest and toughest in the world, so most work gets done collaboratively."
Duncan has a B.S. in mathematics from the University of Arizona, an M.A. in mathematics from the University of Michigan, and a Ph.D. in mathematics from the University of Illinois. He had a successful professorial career at a state university, but local problems at the university were making it increasingly evident that a move was needed. He joined the CCS in 1986, soon after it opened.
"What I do now is not all that different from the research side of my professorial life," he says, "and in many respects this is the ideal sort of position for me. My background in number theory and in computing in number theory meant that I was always unhappy with run of the mill computers that were designed for floating point computations, and I was always interested in the various tricks and quirks of machines that allowed one efficiently to compute things in discrete mathematics. Much of NSA's work is in discrete mathematics, integer arithmetic, and bit-pushing, all of which I did as a professor. And, since I was always at least as interested in actually computing things as in proving theorems about computing things, the fact that we at CCS need to get real results is nothing new--I was always interested in the constant in the big-O as well as in the asymptotics."
"I would strongly recommend that today's students balance a background in pure mathematics with courses in computer science, applied mathematics/numerical computing, the hard sciences, or even electrical engineering. Most mathematicians in industry are probably going to spend their time formulating mathematical solutions to analytic problems in science or engineering and then participating in the computational evaluation of those solutions."
"Working in industry requires that you stay flexible. Don't be afraid to admit you don't know something but could learn. It's a virtual certainty that what you wind up doing in industry will be different from what you learned in classes, but if you're smart enough to get through a mathematics curriculum and have obtained the general education that has taught you not what to think but how to think, then you should be able to expand your knowledge of details while still being a productive employee."
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