**by Richard J. Shaker**

from the *Notices*, May/June 1992 p. 408-411

Richard J. Shaker is Chief of the Office of Mathematical Research at the National Security Agency (NSA). Following are excerpts from his address at the Joint Mathematics Meetings in Baltimore on January 8, 1992.

I work for a wonderful agency that does marvelous things we cannot tell you about. Our public affairs office is paid for the number of column inches that do not appear rather than the number that do. They were pleased when the program listed my affiliation as the National Security Administration, although they would have preferred Social Security Administration (or our most common mistranslation, the National Aeronautical and Space Administration). Throughout this Baltimore area, thousands of individuals tell store clerks or Department of Motor Vehicle officials that they work for the Defense Department---the among those clerks say, "Oh, you mean NSA." Our Director, a charming, wonderfully people-oriented leader, makes but two or three public appearances a year. Yet, one of Admiral Studeman's rare appearances in 1989 was to address these societies, then convened at Phoenix. Mathematicians are now instructed to display the National Security Agency, rather than the Defense Department, on their name tags when attending professional meetings. This exception from anonymity for mathematicians and mathematics by an agency that craves anonymity was not given lightly---only after we realized that mathematics, a vital resource for the United States---a resource essential not only for our industry and science but also for our security and defense---was not receiving support commensurate with its national importance.

Even more than in the forties, when the great mathematicians played vital roles in the dramatic successes of cryptanalysis during World War II, mathematics is the fundamental science supporting the creation and analysis of the complex algorithms that protect vital communications. Not surprisingly, the NSA has a constant requirement for mathematicians in our work. We need well-trained mathematicians not simply because they are well trained in the deductive thinking needed in cryptanalysis---we need them because graduate-level mathematical concepts, ideas, and theorems are needed to solve our problems When pressed to describe mathematical subjects especially useful to us, we list algebra, number theory, combinatorics, probability and statistics, but, in fact, every important subject area in core mathematics has proved valuable. Our mathematicians have used both the mathematics they have known well---their area of specialization---or the mathematics with which they were merely familiar---areas in which they had a single graduate course, or studied for the first time after coming to NSA---to solve our problems. When selecting mathematicians for hire, we are not overly influenced by their area of specialization: we look for a solid record of accomplishment in core mathematics and evidence of strong problem solving ability. Besides using mathematics to solve our current problems, after solving them, we use mathematics to understand what we have done. The abilities of mathematicians to abstract, to generalize, to characterize, to prove theorems, are all important to us. We have several examples where an idea or a technique used to solve one problem has been developed into a major internal NSA subject matter, a local paradigm, used for over a decade to solve a number of other problems more important than the original problem ...

It is well known that we do a great deal of computing on a number of state-of-the-art computers; less well known that our top programmers are pure mathematicians who can, at a moments notice, turn off their programming skill and work in the rarified atmosphere of pure mathematics, though their most typical mode is to do both simultaneously. The relationship between empirical and theoretical is synergistic, with neither driving the other out. No matter how powerful our computers, we need them to be more powerful. Our best cryptomathematicians make them more powerful with subtle coding and aggressive use of leading-edge architectures. When needed, our mathematicians have taken the lead in designing special purpose computers for especially effective cryptanalytic applications. To do this, they have had to learn new concepts and subject matter, but their understanding of the cryptanalytic problem and the underlying mathematics has been indispensable. Although they have worked closely with engineers and computer scientists, they could not be replaced by them.

Clearly, we need a healthy U.S. mathematical community as a source for technical staff. More subtly, we need a healthy U.S. mathematical community because no matter how skilled our staff are, and how well they are able to apply mathematical technology to cryptologic problems, there are always important new developments in mathematics that seem very abstract, that seem unrelated to what we are doing, but through some miracle (sometimes referred to as the "unreasonable effectiveness of mathematics") are exactly what we need to solve the important problems of the present. For our access to the cutting edge of the "new mathematics" to be most effective, we require a strong U.S. mathematical community to help keep us informed, and we can best learn from you if you can take the time to learn what we do. We have benefitted greatly from visiting academic mathematicians who have worked directly on our problems, in a succession of summer conferences, or on their sabbaticals, or as consultants. They have solved important problems and enhanced our old technology, but, more importantly, they have played a vital role in exposing us to new ideas and new mathematics, some of which we have continued to use for many years.

I am going to describe 1987 as the beginning of a time period when, because of concern for the health of mathematics in the United States, we began to overcome our introspection and circumspection and "came out of the cold" to become more active citizens in the mathematical community, but we have had important interactions with mathematics throughout our four decades.

In 1987, we opened up the NSA twice, for two days each, to 100 leaders of the U.S. mathematical community, letting them into the "Puzzle Palace" without requiring them to fill out extensive forms, be fingerprinted, or take a polygraph examination. Some thought that the reason for these conclaves was a dramatic announcement: that we intended from our limited technology budget to provide $2--$3 million annually in grant funding for undirected (by us) mathematical research. I was pleased to have been correct in my prediction that our 100 visitors in 1987 would be more interested in us than in our money. Several of the visitors commented to me that the most important thing they learned about NSA was that it was populated by the same kind of people they worked with in their universities, which they meant neither as praise nor criticism.

In a two hour discussion period during the first of the two 1987 meetings, you gave us guidance on how we should administer our new grants program. Many of our visitors had a lot to say. Everyone seemed to have a pet project, an area, an initiative, or a niche where funding was needed, funding which would have great benefit to the research community and thus to the health of American mathematics; yet funding that for some reason was not being provided by anyone else. We listened intently and constructed our program accordingly. We have continued to listen. Under the leadership of Brent Morris, Marv Wunderlich, and Charlie Osgood, we have, for four years, been running a program that the David II report praised, not only for helping in dollar terms reverse the severe downward trend of government funding of mathematics in real dollars, but for providing the funding in innovative and worthwhile new programs.

NSA has undertaken a number of new initiatives following the 1987 meetings, in addition to our grants program and increasing participation in open research and national meetings. We have established a formal sabbatical program so that you can visit us, work with us for a year or two, and continue to remain affiliated with your university and participate in your university's retirement program. We have also constructed a program for NSA mathematicians to return to academe. We committed, early on, to provide core funding for the Mathematical Sciences Education Board (MSEB), and, better than money, sent them one of our best and most energetic mathematicians, Kevin Colligan, on a one-year, non-reimbursable detail. With mixed feelings, we said goodbye to Joan Donahue, a fine mathematician, technical manager, and leader of our educational reformists, who left us to become a full-time member of the MSEB staff. We built on our MSEB connection by meeting through them and becoming involved with the National Council of Teachers of Mathematics, the Alliance to Involve Minorities in Mathematics, the [Mathematical Association of America's] SUMMA committee, and other national-level efforts. We have been active in outreach programs to historical black colleges and universities and other minority institutions; this year, many of our mathematicians will be involved in HBCU/MI (Historically Black Colleges and Universities/Minority Institutions) support efforts. We participate in a wonderful program, the National Physical Science Consortium, where we support a number of new women and minority mathematicians each year for up to six years through their Ph.D.\ studies---more important than merely sending checks, we meet the fellows, expose them to the excitement of NSA problems, and mentor them. At the state level, we have been a key player in the early efforts to establish the Maryland Mathematics Coalition, a broadly representative group of government, industry, and education leaders promoting mathematics education reform throughout the state.

I want to discuss in more detail two NSA programs that contribute to the health of American mathematics, that play to our strength and that are new since 1987. The first is a cherry-picker program. It hopes that despite all that is wrong with our educational system, we can discover some gems near the end of the pipeline and provide that last little push to get them through. It is a program where it is easy to see accomplishments. The second is harder. It is like throwing a pebble in the ocean. It is more controversial.

The first intervention program [the Director's Summer Program (DSP)] I want to tell you about belies the notion that we have problems with our educational system.

We began in late 1989 to aggressively seek out top young undergraduates who showed great promise and interest in mathematics and expose them to our exciting problems. Many thought we were doing this as a long-term recruiting program. Indeed, we were recruiting, but for mathematics, not for NSA. Our interest and intent was to use a summer experience with us, preferably between the junior and senior year, to provide direct evidence that mathematics provides both subject matter and training for challenging careers. We had hoped for a few more, but we were still pleased that eight were able to stick it out through the processing and come, because they were eight very special young people.

We were hoping that we could put these eight in a room by themselves, working on our best problems, so that the experience would be strongly peer-interactive, but such an aggressively structured experience could only be pulled off if our top mathematicians took on technical director responsibilities. The demands on our top mathematicians are incredible. They have too much to do, they have earned the right to do what they want, they most enjoy solving our hardest problems, they are most rewarded for the work they do in solving our problems. Yet, the first two of our top mathematicians that we asked to lead the 12-week DSP not only said yes, they worked hard during the spring to prepare for the students, identifying and developing the best problems to present them. When one of them was asked how he had the time to nursemaid eight students, he responded, "Did you see their resumes?"

The first two weeks of the workshop were extremely difficult, for the technical directors and the students. The students had to learn decades of NSA-developed technology in two weeks, as well as a myriad of details about the four problems presented them. During these two weeks, some learned to program for the first time. All were proficient programmers by the end of the summer. One, who had no computer science courses on his transcript, taught everyone C in half a day. Another, who also had no computer science courses on his transcript, didn't like our setup and so wrote a special operating system for the group. By the third week, the students knew everything there was to know about the problems, had developed their own suite of programs, had broken into overlapping groups, and knew NSA slang and jargon so well they sounded as if they had worked for us for ten years. We had five Sun terminals connected to the CRAY in the room for the eight students and two technical directors, but we had to add three more. Optimists like me expected the students would make substantial contributions to all the problems they worked on. They did. We expected them to come up with innovative, new ways of looking at our problems. They did. We did not expect them to obtain significant bottom-line results. That's where we were wrong. On the fifth and tenth weeks, they obtained very important results substantially solving two of the problems, convincing the last of the skeptics that this program was very worthwhile. Clearly, we were rewarded for trying to do a good thing. But the real payoff was not the contributions to our product, impressive as those contributions were. The real payoff was to the pipeline.

Incredibly, before they met us, two of our DSPers, juniors, had not been planning to go on to graduate school following their senior year. They had outstanding academic credentials. Some of the others had been off to faster starts, taking an incredible assortment of undergraduate and even graduate level courses while in high school. But these two were performing exceptionally well in their current, demanding academic program, and, ironically, made the most direct contributions to the most significant bottom-line results of the workshop. One, according to her father, might have gone on after taking a year off or might not have. But she came home from the DSP with a surge of confidence, applied to all the top graduate schools, and is now in a Ph.D. program on a National Science Foundation (NSF) fellowship. The other had no intention of going on. After two weeks, she wanted to become an NSA employee. She would have been a fine one, and still may well be one, but we talked her out of joining us right away. A joint math, computer science major through her junior year, she took all pure math courses her senior year and is now in graduate school in a Ph.D. program on a fellowship.

The 1991 DSP was also very successful. We had more time to canvass the nation systematically, which we did through the good auspisces of the MAA. With the 1990 success, it was easy to recruit top technical directors. They led a larger group of participants, including some 1990 returnees, to complete solutions to three problems and significant results on four others.

The second, broader NSA initiative we now call the NSA Mathematics Education Partnership Program (MEPP). Inspired by the 1987 meetings, our mathematicians, some of whom had been active in educational support projects earlier, initiated, doubled, or redoubled their efforts. NSA volunteers went to high schools to talk on mathematics, cryptology, and other exciting applications of mathematics. As they built up their courage, they dared to venture into the middle and elementary schools, where it was scarier to talk to the students, because they were so young and so small, but where the potential impact was greater. In response to numerous requests from the schools that we visited for a list of talks we were able to give, one mathematician volunteered to produce a brochure listing all the talks all NSA mathematicians were willing to give. He discovered through a nightmare year how difficult it was to prepare such a brochure. But his effort led to a well-defined speakers' bureau with a fixed set of offerings, along with an expressed willingness to prepare customized talks at teacher's requests. The popularity of this program built over the years---in 1991, NSA speakers made 230 forays into the three local counties, often presenting multiple talks. NSA was approached to find volunteers for coaching mathematics teams in high schools, to lead science enrichment programs in elementary and middle schools, and to provide faculty at summer mathematics camps for gifted and talented students. For each program, volunteers were identified and NSA management supported these efforts. At our initiative, our mathematicians presented two three-day workshops to middle and high school teachers on the application of mathematics to real world problems.

After four years of active volunteer activities, a thousand points of light, we have decided that our support of K--12 is important enough to institutionalize it. Last month, Admiral Studeman formally established the MEPP after fifteen senior mathematicians representing all the NSA mathematical elements prepared a hard-hitting, enthusiastic report urging creation of the office. We will continue to depend on the spirit and enthusiasm of our hundreds of volunteers, but we believe there are benefits to establishing a single contact point and employing a small staff of mathematicians in full-time planning and coordination. At a time of austerity, when we do not have enough mathematicians to tackle the expanding number of problems we face, it takes a sense that educational support is very important to dedicate even three mathematicians to the program. We are also proud of who they are---one senior and two mid-career mathematicians taking two years out from successful careers breaking codes, then to be replaced by other working mathematicians.

Just as in the greater mathematics community, these activities began in controversy at NSA, not the result of concerns of lawyers or agency managers, but concerns of working mathematicians that we should not get involved, that we're not the right people to help solve the problem, that the problems are too hard, that they're beyond our scope, that they're societal problems, that we have a job to do, that we're being paid to break codes, that "real mathematicians don't do K--12." But as we have convinced ourselves that our long-term health is our concern and that we do have something to offer, we have ignored those voices rather than argued with them, and we have really had a wonderful time. The excitement of contributing to the long-term health of our profession and the satisfaction that comes from sharing our excitement about doing mathematics is a real reward that more than makes up for time "away from the job." In the same way that presenting twelve talks in Baltimore is perhaps more important for us than it is for you, these outreach activities that I've described help us understand the importance of belonging to a larger community and continuing to contribute to our profession.

Now that you know we're good guys, you'll be pleased to hear that we're not going out of business. Cryptology remains a vital mission. The world is still a dangerous place, a volatile place. The need for our decision-makers to be as well-informed as possible has not diminished. But I would be less than candid if I did not admit that we are facing more then a little bit of austerity. It has not yet gotten to the point where we have to conduct a bake sale or collect grocery receipts to buy our computers (we do collect grocery receipts for the local schools), but although NSA is a national agency with a national mission, a large part of our mission supports Defense, so we cannot expect to be immune from the draw down taking place in Defense. But the consistent ability of mathematicians to understand and solve the difficult problems we face has encouraged our management, very few of whom are mathematicians, to prioritize the hiring of mathematicians first and foremost.

As an insular NSA cryptologic mathematician, I believe cryptography is a unique subject perfectly suited for the science and art of the mathematician. But can it be all that unique? Our mathematicians do more than classical cryptology. They have proved indispensable in project areas they might never have been exposed to had we not been bringing on mathematicians for cryptography and cryptanalysis. They provided big breakthroughs needed for our work in communications, engineering, speech research, signals processing, and the design and implementation of powerful, specialized computers. In doing this, they worked closely with engineers, computer scientists, physicists, and linguists. Although at times distinctions in background blurred as scientists worked on common problems, the ability of mathematicians to understand mathematical foundations and employ mathematical analysis has been vital. Appreciation and respect for mathematicians among NSA managers who do not have hands-on experience in cryptanalysis and cryptography comes in part from respect for the cult of the codebreaker but, also, and significantly, in part from the demonstrated usefulness of mathematicians on projects that managers understood quite well but had not realized mathematicians would be so useful on; perhaps did not realize they would be useful at all.

Just as the David committee understood it was naive to expect that the government would discover on its own the need to fund research in mathematics, it is naive to believe we can sit back and have industry discover mathematics. NSA can help a little by sharing the message it has brought here with the captains of industry---it does try to do this, whenever it can, but perhaps it needs to do this more systematically, more deliberately. Perhaps your "power structure" can lobby industry or, further up the pipeline, the business schools, educating them on the value of mathematicians in yet another outreach program. Mathematicians in industry need to convince their management, when they do a fine piece of work, that they have been able to do it not just because they are brilliant but because they are mathematicians. National and state consortiums of employers of mathematicians to support education can add "employment" to their agendas, as I understand the Maryland state coalition has. But without waiting for others, there is much you can begin to do at a "grass roots" level. At a minimum, we need enhanced awareness on the part of research mathematicians of how mathematics is used in industry. We need top research mathematicians to take occasional sabbaticals in industry so that, if for no other reason, they can develop perspectives and contacts that help them be broader in their ability to counsel their students on employment opportunities. We need Ph.D. advisers to keep in touch with their graduates in industry, as well as their graduates in academia, to learn what they're doing as well as how they're doing. We need mathematics departments to be involved in helping undergraduates find summer jobs working with mathematicians in industry that will encourage them to remain mathematicians. We need Ph.D. advisers to care about what permanent jobs in industry their graduates are taking as much as they care about what faculty positions they're taking. We need our mathematicians in industry to be employed in jobs where they can make a difference, well-mentored to maximize the probability that they will.