Akshay Venkatesh, Robert & Luisa Fernholz Professor in the School of Mathematics, and past Members David Ben-Zvi and Yiannis Sakellaridis have made significant progress "on a long-held dream within a sweeping research initiative in mathematics called the Langlands program."

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Number Theory

Peter Sarnak, Gopal Prasad Professor in the School of Mathematics, has received an honorary doctorate from Stockholm University for his work in number theory and mathematical analysis, which is "famous for great depth and tremendous breadth."

"Earlier this year, a trio of mathematicians decided to make lemons into lemonade — and ended up making major headway on a problem that mathematicians have been thinking about for centuries."

"A mathematician who went from obscurity to luminary status in 2013 for cracking a century-old question about prime numbers now claims to have solved another. The problem is similar to—but distinct from—the Riemann hypothesis, which is considered one of the most important problems in mathematics."

### IAS Scholars Win 2023 Breakthrough Prize Foundation Awards, including New Horizons and New Frontiers

The 2023 New Horizons in Mathematics Prize, a renowned award which honors the work of early-career mathematicians, went to past Veblen Research Instructor Ana Caraiani (2013–16), recent von Neumann Fellow Ronen Eldan (2021–22), and current Member James Maynard.

"In 2013, one of the best—but also one of the worst—things that can happen to a mathematician happened to James Maynard. Fresh out of graduate school, he solved one of the discipline’s oldest and most central problems, about the spacing of prime numbers."

Past and current scholars in the School of Mathematics and Natural Sciences have won four of the prestigious prizes granted by the International Mathematical Union (IMU), including the 2022 Fields, Abacus, and Chern Medals, and the Gauss Prize.

By Alex Kontorovich, Member (2009–10, 2013–14, 2016) and von Neumann Fellow (2017–18) in the School of Mathematics:

"Not long ago, I was asked to explain the so-called Langlands program in a single tweet. Impossible, I immediately thought. It’s one of the biggest, most sweeping projects in mathematics, capable of connecting distant realms of research and, naturally, fiendishly difficult to describe."

Current Veblen Research Instructor Sarah Peluse has been awarded the 2022 Dénes König Prize for the paper "Bounds For Sets With No Polynomial Progressions." The honor is presented to an early-career scholar for outstanding research in discrete mathematics.

"In a recent paper, Manjul Bhargava of Princeton University has settled an 85-year-old conjecture about one of math’s most ancient obsessions: the solutions to polynomial equations such as *x*2 – 3*x* + 2 = 0. 'It’s a great problem, famous old question,' said Andrew Granville, a professor at the University of Montreal. '[Bhargava] had an interesting, somewhat different approach, which was very creative.'"