Introduction

Figure 1.

Photo courtesy of UC Merced.

It’s been over four years since I was interviewed by AMS after being selected for the position of Director of the Division of Mathematical Sciences (DMS). At that time, I was asked about my expectations for the position, and I responded that it was too early to tell. Here, I’d like to recap some of my experiences as division director, including some of the highlights and challenges we faced. Through these experiences, I also discovered some strategies that I think the math community could use to more effectively partner with DMS for the benefit of both.

DMS is the biggest supporter of mathematical sciences research in the United States and accounts for more than 60% of federally funded basic mathematics research. These areas include algebra, topology and geometric analysis, number theory, applied mathematics, analysis, combinatorics, probability and statistics, computational mathematics, and mathematical biology. The annual budget for DMS was $233M when I started in 2018 and grew to $244M in fiscal year 2021. About 73% of these funds go to Individual PIs. Looking at it another way, every year, DMS supports close to 6500 researchers including over 2600 senior researchers, 2300 graduate students, 380 postdocs, and 1200 undergraduate students. In terms of the number of proposals, DMS also handles one of the largest portfolios at NSF, managing over 3000 proposal reviews annually, yielding around 750 awards per year.

Research Highlights

An important role for the division director is to champion the value of mathematics research. Throughout my time at DMS, I found that developing new partnerships with other directorates was an excellent means of achieving this. One important initiative was the 10 Big Ideas started by the NSF Director France Cordova. DMS responded by actively participating in three of the Big Ideas: Harnessing the Data Revolution (HDR), the Rules of Life, and Quantum Leap. In the HDR Big Idea, DMS was involved in the Transdisciplinary Research in Principles of Data Science (TRIPODS) and the TRIPODS Institutes. By design, each of the awards had mathematicians playing a major role in the team. We also participated in the Rules of Life Big Idea through the NSF-Simons Research Centers for Mathematics of Complex Biological Systems program. Partnerships weren’t restricted to the US either. We initiated two new partnerships, one with the UK and another with Israel to jointly fund proposals that supported collaborations between PIs in those two countries.

One unexpected challenge was the COVID-19 pandemic, and it would be hard to overstate the effect that it had on the operations of DMS. We had to transition to full virtual panels and the staff moved to full remote telework within a few weeks. As the normal means of meeting with PIs was no longer viable, we sought out new ways to engage with the math community. One initiative was a new monthly DMS Virtual Office Hours. Starting in October 2020, we averaged about 150 participants at each session. Topics ranged across all the DMS programs and included news updates from NSF, MPS, and DMS.

In direct response to the pandemic, NSF was provided with additional funds to address the challenges the country faced. In turn, NSF issued a call for proposals in the spring of 2020 to address COVID-19. Watching the math community respond to our request for proposals was one of the most rewarding events I’ve ever participated in. In the end, we were able to fund 20 proposals that led to novel approaches to understanding the spread of the pandemic as well as new methods for understanding the disease itself. Because of the overwhelming response to this call, the following year DMS cohosted a workshop with the Social, Behavioral, and Economic Sciences directorate that sought to develop new epidemiological models in collaboration with social scientists.

Two other initiatives that I believe will have a long-term influence came out of an earlier partnership with the Simons Foundation and involved the rapidly growing field of Deep Learning. This led to a new program on the Mathematical and Scientific Foundations of Deep Learning (MoDL) in 2020. While other programs existed in this area, none of them addressed the foundational or theoretical aspects of the field.

Training Opportunities and Broadening Participation

One recurring comment I heard from the community was the difficulty in providing support for graduate students. This troubled me, as I’ve always believed that we must provide support for our early-career mathematicians to ensure a healthy profession. As a result, we decided to increase funds in this area. In 2019–2020, DMS invested $20M toward graduate student support, which resulted in an additional 675 graduate students funded on research fellowships.

DMS also participated in two new programs aimed at early-career PIs, the ASCEND and LEAPS programs. The ASCEND program supports postdocs who will help broaden the participation of groups that are underrepresented in the mathematical and physical sciences. The LEAPS program, supports the research of early-career faculty and is focused on those working at institutions such as minority-serving institutions, predominantly undergraduate institutions and R2 universities. I believe that both programs are a great step toward increasing the diversity of the math community.

One observation I had when I arrived at DMS was that there was a lack of diversity in program officers. During my initial discussions with the program officers, this subject kept popping up, especially with regard to gender diversity. This led to several discussions at our weekly staff meetings, where everyone agreed that we needed to emphasize gender diversity within our own ranks. When I arrived, there were three women program directors. By 2022, we had a 50-50 split of men/women program directors. In my last year, we hired seven rotators, of whom four were women and two were underrepresented minorities. In total, during my time at NSF, we hired 26 rotators, 16 of whom were women and four of whom were underrepresented minorities. I’m happy to see that this trend has continued, and today the division stands at 27 program directors, with 16 being women—a true team effort by everyone at DMS.

Recommendations

Based on my experiences, I found that DMS has done an exceptional job in serving the mathematics research community. I take heart that the Committee of Visitors, which reviewed the programs in DMS agrees with that assessment. Nonetheless, I believe that both DMS and the mathematical community can do better in terms of making the case for mathematics research in the country. In what follows, I make several recommendations that I hope will start some discussions between all the parties involved.

My first suggestion is that the math community should take additional steps to partner more effectively with NSF, and DMS in particular. From the perspective of NSF, input from the community is highly valued and important, especially during budget discussions. Other directorates have active constituencies—astronomy and computing sciences for example. In astronomy, the community produces a decadal survey prioritizing their large facilities. In computing, the Computing Research Association (CRA) produces quadrennial papers that provide potential research directions, challenges, and recommendations. AMS should consider doing something similar. Many of the internal discussions at NSF revolve around the needs of the scientific communities and having such reports provides important reference points.

The math community already engages DMS through various science policy committees and the Government Relations Office. The science policy committees are a good start, but they generally only meet once a year. More frequent and active partnerships would enhance relations. Professional societies could play an important role in collecting and championing new research areas. Congressional briefings are another excellent idea, and the work of Karen Saxe, head of government relations at AMS, is always appreciated. AMS has a unique ability to take the pulse of the math research community and to elevate important new research areas to the attention of NSF and DMS.

Another avenue is through convening workshops on current research trends. I already mentioned the DMS-funded workshop on Research on Enhancing Socially and Behaviorally Modulated Mathematical Models for Human Epidemiology. Other examples included the workshops on Statistics at a Crossroads: Who is for the Challenge?, the workshops on Rules of Life in the Context of Future Mathematical Sciences, and the Workshop Report for Research Training Group Grants. All these reports were instrumental in helping DMS define its funding portfolio.

Finally, I’ll point to the important role that program directors play in the operations of DMS. I encourage those of you who might be interested in serving as a program director to contact DMS about opportunities. I found my time at NSF to be rewarding and I learned much about the state of research (both in mathematical sciences as well as other areas) in the US.

My four years at NSF were a time of great change and many challenges. And they were also some of the best times in my career. Let me end with my heartfelt thanks and deep appreciation to everyone who helped me while I was at DMS. Together we were able to accomplish much, and it was all because of the many people who came together under challenging times to maintain a vibrant and exciting mathematics research environment.