# Update from the Division of Mathematical Sciences

By Michael Vogelius, Tie Luo, and Henry Warchall

With this article, the management team of the Division of Mathematical Sciences (DMS) at the National Science Foundation (NSF) would like to provide an update about recent program activities from the DMS and an outlook for the future. The DMS plays a critical role in providing about 64 percent of all U.S. federal support for basic research at the frontiers of discovery in the mathematical sciences. It also supports training through research involvement of the next generation of mathematical scientists, conferences and workshops, and a portfolio of national mathematical sciences research institutes.

Here we call attention to four recent funding opportunities that we find particularly newsworthy. Two are calls for development of large-scale interdisciplinary research centers/institutes that involve collaboration between mathematical scientists and researchers from other scientific areas, and two are calls for activities to enhance and broaden graduate education in the mathematical sciences.

### 1. Transdisciplinary Research in Principles of Data Science

The Transdisciplinary Research in Principles of Data Science (TRIPODS) program aims to bring together the statistics, mathematics, and theoretical computer science communities to develop the theoretical foundations of data science through integrated research and training activities. Phase I will support the development of small collaborative institutes. Phase II (to be described in an anticipated future solicitation, subject to availability of funds) will support a smaller number of larger institutes via a second competitive proposal process. All TRIPODS institutes will involve significant and integral participation by all three communities.

The TRIPODS program is a part of the NSF initiative “Harnessing Data for 21st Century Science and Engineering,” one of the “10 Big Ideas for Future NSF Investments.” It is co-funded equally by the NSF Division of Computing and Communication Foundations and the DMS. These investments are augmented by funds from the “Growing Convergent Research at the NSF” initiative and the Office of Multidisciplinary Activities of the Mathematical and Physical Sciences Directorate. It is the hope of the DMS that the TRIPODS program will emphasize to academic institutions forming programs in data science that such efforts naturally involve computer scientists, mathematicians, and statisticians. The TRIPODS Phase I proposals are currently under review, and it is anticipated that up to 12 three-year awards of approximately $500,000 per year will be made.

### 2. NSF-Simons Research Centers for Mathematics of Complex Biological Systems

The NSF-Simons Research Centers for Mathematics of Complex Biological Systems (MathBioSys) is a new program that expects to fund centers of five-year duration from a one-time call for proposals. The program focuses on research to understand emergent properties in biological systems. It welcomes proposals to establish centers at which sustained collaborations are facilitated between mathematical scientists and biologists to develop novel mathematical, computational, and statistical approaches. Such approaches will advance fundamental understanding of how and why emergent properties arise in molecular, cellular, and organismal systems. The program strongly encourages projects aimed at developing predictive frameworks for understanding phenotypes. Projects are expected to include plans for significant effort in cross-disciplinary training of cohorts of future scientists, such as postdoctoral research associates, graduate students, and/or undergraduates from mathematical sciences and related areas of the biological sciences. Each center is also envisaged to conduct convening activities, including short-term and/or long-term visitors’ programs, workshops, and/or outreach activities.

The MathBioSys program is part of the NSF “Understanding the Rules of Life: Predicting Phenotype” initiative, another of the “10 Big Ideas for Future NSF Investments.” The program is co-funded equally by the Simons Foundation and the NSF, with 30% of the total investment furnished by the DMS and 20% furnished by the NSF Directorate for Biological Sciences. Letters of intent and proposals are due August 10 and September 29, 2017, respectively. It is anticipated that three centers devoted to collaboration between mathematicians, statisticians, and biologists will be funded. Each center will be funded for a five-year duration with an annual budget of $2 million.

### 3. Mathematical Sciences Graduate Internships

By means of this activity, the DMS aims to provide opportunities to enrich the training of graduate doctoral students in the mathematical sciences through summer research internships in nonacademic settings. The DMS has partnered with the Oak Ridge Institute for Science and Education (ORISE), which is managed by Oak Ridge Associated Universities for the Department of Energy, to establish the Mathematical Sciences Graduate Internship program.

The immediate goal of the program is to arrange and support internships for approximately 40 students annually, primarily at U.S. National Laboratories. The program is intended to introduce doctoral students in the mathematical sciences to important applications of mathematical or statistical theories outside of academia. The internships are aimed at students who are interested in learning about such applications, regardless of whether they plan to pursue an academic or nonacademic career. Interns will not only gain experience in the diverse uses of advanced mathematical tools at National Laboratories, but also become aware of the additional skills required for success in employment outside the traditional academic setting. The program is equally intended for students in pure and applied areas. It is planned to continue this collaboration with ORISE in 2018.

### 4. Improving and Supporting the Transition to Graduate School in the Mathematical Sciences

The NSF Directorate for Education and Human Resources and the DMS invite proposals for projects designed to encourage and prepare U.S. students to pursue and succeed in graduate doctoral study in the mathematical sciences. Particular emphasis is placed on broadening participation of students from underrepresented populations, including racial/ethnic groups underrepresented in mathematics and statistics, individuals with disabilities, and women. The activity aims to support projects that are scalable—to serve large numbers of students without large increases in cost—and sustainable, that is, have continued impact without ongoing large influxes of grant funding. Projects are expected to involve mathematical sciences research as part of student training, and/or educational research that produces new knowledge to help the community understand for whom—and under what circumstances—proposed activities are effective in preparing a diverse population of students to be successful in graduate school.

### About These New Initiatives

The DMS considers the first two aforementioned activities to be parts of the DMS research institutes portfolio, which currently constitutes approximately 12 percent of the annual DMS investment. These new opportunities represent the continued evolution of the DMS institute portfolio, which the division aims to keep current, dynamic, and responsive to emerging needs of the mathematical sciences community. Both new programs were developed in close consultation with the communities involved, in particular through workshops that provided insight into current activity in these areas and perceived future needs. Both new programs are centered on an intellectual partnership between the mathematical sciences and another discipline, matched by significant financial investment from the other disciplinary partner. This arrangement reflects the worth of the interdisciplinary activity from a scientific viewpoint, in that it certifies the importance of these activities to both disciplines. It also greatly leverages DMS investments. The DMS is particularly pleased to be able to initiate a close partnership with the Simons Foundation in support of the new MathBioSys program.

The DMS considers the third and fourth activities to be parts of the DMS workforce program portfolio, which currently constitutes approximately 10 percent of the annual DMS investment. These new opportunities address two distinct community needs in support of the development of the next generation of mathematical scientists. First, employment data show that the majority of mathematical sciences Ph.D. recipients take employment other than conventional academic tenure-track positions; yet many U.S. graduate programs in the mathematical sciences do not provide students with needed information about potential nonacademic career paths. The Mathematical Sciences Graduate Internship program is an early step towards raising doctoral students’ awareness of potential, rewarding nonacademic careers. Second, despite substantial efforts by the mathematical sciences community and investment by funding agencies, current data indicate that both the percentage of women and the percentage of students from underrepresented groups entering doctoral programs and receiving doctoral degrees in the mathematical sciences have remained relatively constant since 2004. These levels are well below the representation of these groups in the general population. The activity in Improving and Supporting the Transition to Graduate School in the Mathematical Sciences aims to catalyze cost-effective community projects based on proven techniques to address this underrepresentation.

### Outlook for the Future

As of this writing, the Congressional appropriation for the fiscal year 2017 budget has not been finalized. The expected fiscal year 2017 budget for the DMS is $233,512,000, which represents a small decrease of approximately $400,000 from the 2016 level. The President’s fiscal year 2018 budget request to Congress for the NSF will result in a decrease in the DMS budget of approximately $24,000,000, roughly a 10 percent reduction. The highest priorities for the DMS in this challenging budgetary climate are to maintain—to the extent possible—investments in its core activities, namely the disciplinary programs that fund unsolicited proposals for research by individual investigators and the research institutes portfolio.

Looking further into the future, the Mathematical Sciences Research Institutes program will hold an open competition in fiscal year 2019. Proposals are invited for new institute projects from U.S. sites, as are renewal proposals from any of the currently-supported U.S.-based Mathematical Sciences Research Institutes. Awards from this competition are anticipated to begin in fiscal year 2020. The DMS is committed to maintaining investment in its research institutes portfolio at a level of 12-14 percent of the total DMS investment over the long term.

Michael Vogelius is the division director of the Division of Mathematical Sciences (DMS) at the National Science Foundation. Tie Luo is the deputy division director of the DMS. Henry Warchall is the senior advisor at the DMS.