## An Auspicious Beginning for NSF's 2002 Math Sciences Initiative

**December 21, 2000**

In his final column as SIAM president, Gilbert Strang bases his optimism in part on recent developments at the National Science Foundation: a 13.6% increase in the NSF budget for fiscal year 2001 and a proposed Mathematical Sciences Initiative for FY 2002.

Philippe Tondeur, director of NSF's Division of Mathematical Sciences since July 1999 (and to all appearances Strang's equal for optimism), attended an early-November meeting of the Joint Policy Board for Mathematics to discuss the initiative and strategies for building support within the community. Among the factors placing the initiative in an extremely good position is the identity of one of its most enthusiastic advocates: NSF director Rita Colwell.

Colwell made extensive public comments in support of the initiative on at least two recent occasions: the October 19 meeting of the National Science Board at which DMS program director Deborah Lockhart presented the initiative and, on November 10, a plenary session at the Chairs Colloquium of the Board on Mathematical Sciences. Citing the need for advances in mathematics to meet the growing requirements of other disciplines, Colwell called for an increase in the amount and duration of mathematics grants, from the current median of $30,000 per year for three years, and funding for larger numbers of graduate students.

The funding shortfalls, combined with the lure of lucrative jobs in industry for quantitatively oriented undergraduates, have resulted in a serious drain on the field. For the period from 1997 to 1999, Colwell told the BMS audience, the numbers of graduate students in the mathematical sciences decreased by 21% (all students) and 27% (U.S. students). During the same period, numbers of upper-level undergraduate majors in mathematics declined by 23%.

In the BMS talk, Colwell reminded the audience that what is needed from the research community above all is support for the NSF budget---without an overall funding increase for NSF, the impact of an initiative would be modest. She then proceeded to present an array of examples of scientific advances in which mathematics has played a significant role, from faster storm predictions to improved interpretation of medical images via level set methods. The examples would be impressive under any circumstances but become all the more forceful when put forward by a microbiologist.

The initiative, as presented by Deborah Lockhart to the National Science Board, has three distinct components: (1) fundamental research in the mathematical sciences; (2) interdisciplinary collaborations involving mathematical scientists, scientists from other disciplines, and engineers; and (3) mathematics sciences education. "As the role of mathematics has expanded in science and society," Lock-hart pointed out, the resources allocated to these three areas "have not kept pace." The initiative calls for a five-year investment, beginning in 2002, to "spur inter-related efforts on all three frontiers at once."

Preferring the categories "fundamental" and "interdisciplinary" mathematics to the traditional "pure" and "applied," Tondeur points out that the two sets of terms are not exact synonyms for each other. The fundamental research component of the intiative is situated in the context of beneficial linkages to interdisciplinary work; successful examples cited in presentations about the initiative include research in logic and combinatorics as the basis for models of computation and the P vs. NP problem, knot theory in DNA enzymology, and complex analysis and the theory of Cauchy integrals in tomography and data analysis. Fundamental research themes envisioned for the initiative include dynamical systems and PDEs, geometry and topology, stochasticity, number theory, algebraic and quantum structures, the mathematics of computation, Bayesian estimation, and multiscale and multiresolution analysis.

The interdisciplinary component, Lockhart said, is predicated on a "dramatic demand for new mathematical and statistical techniques" in all the sciences and in engineering. It is with this component that the initiative becomes an NSF-wide activity. For this part of the initiative in particular, Tondeur emphasizes the need for partnerships between DMS and virtually all directorates at NSF.

In presenting the third component, the part of the initiative explicitly related to education and mathematical literacy, Lockhart pointed not only to the need to attract larger numbers of talented students into graduate and postdoctoral programs, but also to the role of the mathematical sciences in producing "an educated populace . . . and a well-equipped workforce at all levels."

"It would be impossible to be in a better position," Tondeur told the JPBM members. The director of NSF is advancing support for mathematics as her top priority: Within the framework of a doubling for the NSF budget, she is proposing to increase funding for the mathematical sciences twice as fast. The Mathematical Sciences Initiative, moreover, is the only new initiative for 2002. At the BMS meeting, Colwell called on the community to furnish additional examples of mathematical success stories to Tondeur, who will integrate them into the position developed in support of the initiative.