Andrew Mayer is a research staff member at the Center for Communications Research (CCR), San Diego, California, in a part of La Jolla known locally as the "Golden Triangle." CCR and a similar center located in Princeton, NJ, conduct mathematical research in support of the cryptologists at the National Security Agency.
"Our research staff consists of around 20 full time people," says Andy. "Most of the staff have a Ph.D. in mathematics. There are also numerous consultants and summer visitors in a variety of related disciplines (mathematics, computer science, physics, etc.). We have a small support staff that includes an excellent group of systems administrators, since much of our work is computer related. There is a great deal of collaboration among the researchers here, but there is no official organization into teams or groups. This leads to an enjoyable research environment. I have the opportunity to make contributions to problems that many people want to see solved. Nearly every project I've worked on has been a joint effort, and any competition is of a purely friendly nature."
"Mathematics is the primary tool used in the design and analysis of algorithms for enciphering vulnerable communications, and as a result there are many interesting and important open problems. In every problem we work on, mathematics plays an essential role, whether in the form of new results, or applications of known techniques. Unfortunately, the proprietary nature of most of our work prevents me from providing a detailed example."
Andy has a B.S. in mathematics and physics, from Yale University, and an M.S. and a Ph.D. in mathematics from Princeton University. He spent three summers at CCR, Princeton, before he completed hisPh.D. in 1993 and was then given a two-year term position at CCR, La Jolla. "During this time," he says, "management would decide whether to keep me on as a regular staff member or to extend my term for one more year, during which time I would presumably look for work. I am pleased they decided to keep me, so I didn't have to face the job market again!"
"To be fair," he continues, "I should say that at the time I was finishing my thesis, I had no competing offers from major academic mathematics departments, and I might have accepted one if I had. In retrospect, though, I'm glad I ended up where I did. The areas of mathematics that I like (lattices and quadratic forms, discrete and computational geometry, and some flavors of combinatorics) are applied frequently to the kinds of problems we work on, and, frankly, are not well represented at the top mathematics departments. Moreover, I like to design and implement interesting mathematical algorithms, and we do quite a bit of that, too."
He has the following advice for students interested in a nonacademic position: "First, find ways to collaborate and work with other people. I find that I am listening to half-baked ideas that need to be helped along as often as I am trying to get someone else to listen to my half-baked ideas. I consider part of my job to be finding out what people are doing and thinking about ways I can contribute to their effort. Second, develop good communications skills. I am often called on to describe my work to experts and non-experts, and to write up results clearly enough that people can apply them. Third, rethink your reward structure. Proprietary material often cannot be published. Sometimes brilliant work that solved a particular problem would not even be of general interest. For me, the great reward at CCR is being able to say 'we solved it.'"
"In my opinion, the specific mathematics courses you take are less important than your general problem solving ability," he continues. "A wide variety of specialties are brought to bear on our work, including the following: probability and statistics, finite fields, Fourier analysis, combinatorics, many aspects of number theory, computational geometry, algebraic geometry, algebraic coding theory, finite groups. All of these are good, none necessary. Outside mathematics, I might recommend some courses in computer science (scientific programming, analysis of algorithms, complexity theory), some operations research or economics (optimization techniques), and any electrical engineering you can get your hands on (signal processing, Fourier techniques, coding theory). I want to emphasize that the vast majority of people who work for us don't start out knowing all of these subjects! The important thing is to be able to learn new concepts and to apply mathematics creatively."
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