I do not wish to convey that we cannot make DMS's budget grow; we can and did increase it this year. But the growth will need to be incremental and will come because we have been innovative and are demonstrating careful management of the funds entrusted to us. The mathematical community will need to identify opportunities and help sell them. It probably will need to help identify the more mature areas, and those that have the greatest promise, and be prepared for DMS to do some shifting of funds. As a community, we will need to determine how best to use the limited funds provided to maintain and advance the discipline. This may mean arriving at alternative funding patterns. If we are not prepared to make hard choices, how can we expect others to do so? When the community is willing to make choices and move forward, suggesting areas of opportunity and responding to innovative modes of funding—as, for example, it did for the Group Infrastructure Grants (GIG) program—the foundation does respond with increased funding. The mathematical community must understand the changing environment in which we live, and then be agile in taking advantage of opportunities presented. The purpose of this meeting is to begin the process of taking charge of our destiny.
You should be aware that Congress is now requiring greater accountability of the agencies it funds. The NSF needs to come up with a set of goals and metrics to measure achievement of these goals. Crude counting, whether of students produced, papers published, and so on, will just distort the purpose of the foundation. For that reason it is seeking to have qualitative, rather than quantitative, measurements.
The foundation was founded to promote the progress of science, to advance the national health, prosperity, and welfare of U.S. citizens, and to secure the national defense. The national populace is the foundation's constituency, not the academic research community. Thus it is not sufficient for the NSF to ensure the welfare and progress of academic researchers, confident that their brilliance and hard work will take care of the needs of the nation. It needs to lead the community of researchers and educators in the most beneficial directions for the nation. That being the case, in a qualitative manner we will need to address how our funding has been beneficial to the nation. NSF is funding basic research, and so the time lines for this assessment cannot be one or two years, but since many lines of inquiry will not have a payoff, ever, it will not be convincing to Congress if every investment takes in excess of 50 years before there is any indication that the investment has had a payoff. As Eugene Wigner so ably asserted and demonstrated, mathematics is inordinately effective in its contributions to science—and, as we now know, to management and industry. In the years ahead we mathematicians will need to document this time and time again, and we will need to assist in a faster transfer of knowledge.
As I see it, the mathematics community is going to have to get into the business of telling its story and describing the impact it has had on the general populace, not only to Congress but, to the extent possible, to the person in the street. For far too long, we have been content to communicate individually with a small, select group of colleagues, making little effort to communicate even with the mathematical sciences community as a whole, let alone with our science colleagues. To the educated public we appear to be a small sect, inwardly looking, muttering in an incomprehensible language. If this is the case, how do we demonstrate our contributions to our nation's citizenry?
Our fellow scientists need our help. They need to reduce experimental trials, and they need models to simulate experiments and suggest the most appropriate areas of inquiry. They need the mathematician to help not only in modeling and simulation but also in reformulating their questions. Formulating precise questions is our forte. We have become so inner driven that we have forgotten our ancestry; we forget how much of mathematics was stimulated by physics.