A Math Legend Visits the Next Generation

Every summer, the National Science Foundation and National Security Agency support research programs for top undergraduate students in a variety of federally funded areas of research. These Research Experiences for Undergraduates include one hosted by the University of Virginia’s Department of Mathematics, and last week, the 16 students selected for this summer’s UVA REU in Number Theory got the opportunity to meet and bounce questions off one of the most renowned and influential mathematicians in the world.

Praised for his breakthroughs in partial differential equations, harmonic analysis, number theory and other areas of theoretical mathematics, the Australian-born Terence Tao found himself fielding numerous requests for selfies and group photos from his student admirers in the REU program after concluding a talk on the Collatz conjecture, one of mathematics’ most famous unsolved problems.

“I really like what Terry Tao said about approaching math as if you are speaking to your past self — as a way to explain math to an audience that may include people at all levels of understanding,” said Catherine Cossaboom, a rising third-year student majoring in mathematics and cognitive science and one of two UVA students selected for this summer’s REU mathematics program. “It’s so easy to get caught up in what it feels like to understand something that you forget what it is like to not understand, and his efforts to popularize math through his blog have truly done wonders for the mathematical community through communication.”

A 2006 winner of the Fields Medal — considered the mathematics equivalent of a Nobel Prize — and a recipient of a MacArthur Foundation “genius” fellowship and a raft of international awards, Tao has embraced his role as a public educator, educating mathematics students through his popular website, books and lectures. Most recently, the unassuming Tao, dressed casually in a red polo shirt, dark denim jeans and Birkenstock sandals for his June 15 visit to UVA, accepted an appointment by the White House as co-lead of the President’s Council of Advisors on Science and Technology’s working group studying the opportunities — and risks — provided by generative artificial intelligence.

During a lunch break with REU students, Tao fielded questions about the practical applications of theoretical mathematics and the value of finding those rare opportunities to collaborate with colleagues.

“It’s kind of a shame that you don’t get many opportunities to see somebody else really ‘do’ mathematics,” he said. “It can be a lonely discipline, but it’s only when you collaborate with somebody at the blackboard that it’s a really great experience, when you’re both in the zone and you speak the same language.”

For Tao, one of his most groundbreaking collaborations originated at his children’s preschool 19 years ago. In 2004, another parent and California Institute of Technology mathematician, Emmanuel Candes, mentioned to Tao in the preschool pickup line that he was trying to find a way to reconstruct images taken by an MRI machine with the smallest amount of data. Mulling the seemingly “unsolvable” problem later at home, Tao came up with a solution. Using the algorithms devised by Tao and Candes to reconstruct the rest of the image, compressed sensing has been adapted for a number of uses, including the ability to complete MRI scans more quickly at a lower cost to patients.

“He is such a big deal in the world of mathematics, and he’s accomplished so much even outside that world, we all look up to Terry,” said Samuel Goldberg a rising fourth year at UVA and first-time participant in this summer’s REU program. “At the same time, he has such an unassuming presence that meeting him helps to demystify him. It was almost humbling to meet him, but it was also inspiring to see he’s a regular guy, in a way that makes you feel like you can achieve more.”

‘Optimism for the future’

Ken Ono, UVA’s Marvin Rosenblum Professor of Mathematics and the University’s STEM Advisor to the Provost, has been running REU programs since 1998, including programs held at the University of Wisconsin and Emory University before he joined UVA’s faculty in 2019. He brought his program to UVA.

“My summer program is the highlight of my year. It’s part summer camp. It’s part think tank. The energy and enthusiasm that the kids bring is breathtaking. One kid can solve six Rubik’s cubes while blindfolded!” Ono said. “Despite the many challenges that face mankind, these kids nourish my optimism for the future. I have no doubt that they will one day make the world a better place thru STEM innovation.”

The students accepted for Ono’s program were selected from a national pool of over 700 top students. Participants work in small groups on level-appropriate research projects over the course of the summer program, which offers selected students research mentorships, mini-courses, a weekly colloquium series and professional development activities. Past participants in Ono’s REU program have gone on to earn dozens of NSF Graduate Fellowships and other prestigious fellowships, including Marshall Scholarships, Gates Fellowships, Goldwater Fellowships and Rhodes Scholarships. Former participants include tenured faculty at places like the University of California at Berkeley, Brown University, Harvard University, the University of Chicago and the University of Michigan.

“It can be intimidating, but it has ultimately pushed me to chase after dreams I didn’t originally think were possible,” said Cossaboom, a two-time participant in UVA’s REU program. “I’m thankful for all the support and community this program has brought me.”

Near the end of Tao’s visit to Grounds, he and Ono, who has recently been named to the National Security Agency Advisory Board, met with UVA president Jim Ryan and Provost Ian Baucom to discuss the promise and threat of generative AI.

With artificial intelligence technologies advancing so rapidly in their abilities to generate text, images, videos and other outputs from a given prompt, the PCAST working group Tao is co-leading aims to offer the President background and recommendations for potential federal policies identifying a balance between encouraging innovation and pursuing applications of the technology and identifying and mitigating potential harms such as the driving of misinformation campaigns, and the impersonation of individuals.

“Generative AI could be potentially transformative in many spheres,” Tao said before his meeting with President Ryan and Provost Baucom. “The almost immediate concern, though, is its impact on disinformation and deep fakes and just the erosion of the standard of truth. Already you can use these AI tools to generate realistic images of you and me or President Biden. We already have Photoshop and other tools, with AI, these faked images are much easier to make and harder to detect, and they’re going to start creeping into campaign messages and so forth.”

At the same time, Tao said, the PCAST committee recognizes that in a democratic society, it is not valid to entrust the government with “ministry of truth” powers granting it the final word on what is authentic and what is an inauthentic image or message perpetrated by AI.

“That’s getting too close to censorship. There are First Amendment issues involved, and I’ve had to learn a lot of constitutional law as part of this committee,” he said.