Interview with Ravi Vakil

Every other year, when a new AMS president takes office, the Notices publishes interviews with the outgoing and incoming presidents. Ravi Vakil’s two-year term as president will begin on February 1, 2025. Vakil is the Robert Grimmett Professor of Mathematics at Stanford University.

Q: For those who haven’t met you, please tell us a little about yourself.

A: I’m by nature deeply interested in mathematics. And I very much feel happy as part of something larger than myself, building with other people. For example, I’ve enjoyed creating new mathematics. But helping my students produce even more beautiful mathematics, and trying to change how people enter my field by changing how we think of the subject through writing—hopefully pulling more people into the subject—has been really rewarding.

Figure 1.

Ravi Vakil.

Q: Describe your past service to the AMS. What experiences will you build upon in your presidency?

A: I’ve had a chance to experience many different parts of the AMS. We are arguably the most influential publisher in the mathematical world, and decisions here directly shape the future of the subject. For example, the open access Communications of the AMS is a revolutionary journal that may disrupt the landscape. Math Reviews, and our communal curation of mathematical knowledge, has for decades been a central contribution of the AMS, and is rapidly evolving with the relevant technologies. Our many conferences and programs form the essential core of our community, and I’ve learned that decisions and planning there is much harder than you might think. One thing less obvious from the outside: The AMS staff is hyper-competent.

Q: What challenges do you believe the AMS faces most immediately? What is your plan of action for one or more of these challenges?

A: The main issue facing American mathematics is often misdiagnosed as a series of short-term crises, but it is really a long-term challenge. In contrast with the Sputnik era, the nation is acting like it is in long-term decline. Mathematically speaking, rather than building an interstate system to support the country for decades, we are dismantling it. We are eating our seed corn. How do you convince a country of the importance of intellectual infrastructure, and to act in its own best long-term interest?

The AMS as an institution is as strong as it has ever been, along many axes. To continue to push against this challenge, we need to grow (in member numbers, in breadth) while staying focused on our precise mission, and we need for our active membership to become even more active and interconnected.

Q: What do you think about the AMS’s role in advocacy?

A: The AMS speaks not just for our members, but for all of mathematics. Mathematicians have tended to be shy and retiring about the subject, to the detriment of all society. The direct impact of mathematics is enormous: It has been for centuries, certainly is today, and anyone who tells you that the future will be different is trying to sell you something. Mathematics is at the center of science and knowledge. We make everything else work. We change how people think. Our students (in the broad sense of the word) become mathematical thinkers (in the broadest sense of the word). Society needs more of them; the world is their oyster.

Figure 2.

Jesús De Loera (UC Davis), Karen Saxe (AMS), and Ravi Vakil (Stanford University) visit Capitol Hill in September 2024.

So we need to speak loudly and unapologetically on behalf of mathematics. More of us need to take on the role of “public intellectual.” Even where we do not have enough internal consensus for the AMS to advocate on behalf of the community, we need to get members in the habit of stepping up and engaging. We have been doing more in advocacy (especially our Washington office). We need to take an increasingly public role.

Q: Please share your thoughts about Artificial Intelligence (AI) in mathematics.

A: This is an exciting time, and predicting even a few years out is a fool’s errand. Utopian and dystopian visions put forth by cocktail-party pundits are fun to talk about and attract clicks, but the truly exciting developments require some knowledge to appreciate. Our field has gone through many world-changing technological revolutions, and we know that the flavor of change that is lasting resembles “the internet” more than “flying cars.” I have too many thoughts to fit in my head (let alone this paragraph), but I recommend recent Bulletins of the AMS and Terry Tao’s various commentaries (including his AMS Colloquium Lecture online).

Q: Share with us something we can expect from your presidency.

A: Our community is huge and broad, and we are unified after a period of some division. (i) Decades ago, pure and applied were pulling in opposite directions. We are returning to the traditional view that individually we can deeply specialize, but collectively mathematics thrives only when it is enriched by problems from elsewhere; yet also when it leans into powerful theories one is led to by abstracting ideas to their pure essence. (ii) There was a time when some believed in a sharp division between research and education, but now such a clean break seems bonkers. If you believe in the importance of mathematics, you believe in the importance of spreading it wide and far. There are important unresolved questions about how we work with the wider educational community, but we are now happy to grapple with them. (iii) Everyone agrees that pulling more people into mathematics from all places, and developing mathematical talent in new populations is a good thing. The devil is in the details, of course. In these three cases and elsewhere, we need to model how to disagree as adults; sometimes I am in the minority, sometimes in the majority, but we can be civil and work together.

More generally: I am basically apprenticing with my predecessor, Bryna Kra, who is amazing at this. Although I don’t have her experience and wisdom, I share her point of view, so I expect a continuity of vision. I want to help some of her initiatives grow into adulthood, including programs for undergraduate-facing institutions, and a task force to support departments before they are in distress. I also want to look for opportunities along the lines you can guess from the above—I have “many small ideas” rather than a “few big ones.” The AMS does so much because we have so many volunteers, who are extremely smart and interesting (and fun to talk to); and new ideas work only when led by people who are invested in them. Thus, many of my ideas are attached to specific people, especially younger ones who don’t yet realize that they are now in a position to drive change.