This installment of our “Paths to Math” video series features Kalyani Kansal, Member (2023–24) in the Institute’s School of Mathematics. Watch to hear Kalyani describe her fascination with the “patterns” of the Langlands Program, outline the interesting commonalities between mathematics and detective stories, and discuss the importance of diversity and representation in the field.

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Robert P. Langlands

### 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.

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."

Frequent Visiting Professor Noga Alon has won the 2022 Shaw Prize in Mathematical Sciences for his contributions to discrete mathematics and theoretical computer science. The prize has been compared to the Nobel and carries with it a monetary award of $1,200,000.

"Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that some mathematicians say it—or some aspect of it—belongs in the esteemed ranks of the Millennium Prize Problems, a list of the top open questions in math. Edward Frenkel, a mathematician at the University of California, Berkeley, has even dubbed the Langlands program 'a Grand Unified Theory of Mathematics.'"

George Lusztig, past Distinguished Visiting Professor (1998–99) and past Member (1969–71, 1988, 2020) in the School of Mathematics, has won the 2022 Wolf Prize in Mathematics for his “groundbreaking contributions to representation theory and related areas.”

Camillo De Lellis, IBM von Neumann Professor in the School of Mathematics, has received the 2022 Maryam Mirzakhani Prize in Mathematics from the National Academy of Sciences (NAS).

"Ana Caraiani was given a challenging problem from her adviser, the mathematician Andrew Wiles. He’d recently garnered fame for his 1994 proof of Fermat’s Last Theorem, but Caraiani had less luck with her assigned problem. Still, although she ended up making no significant headway, she remained undaunted."

“It started to feel as if the program was within reach, so in the fall of 2016, to try to make further progress, Caraiani and Taylor organized what Calegari called a ‘secret’ workshop at the Institute for Advanced Study. ‘We took over the lecture room — no one else was allowed in,’ Calegari said."

On May 22, Robert P. Langlands, Professor Emeritus in the School of Mathematics, received The Norwegian Academy of Science and Letters, 2018 Abel Prize, which was presented at the University Aula in Oslo. The Abel Committee cited Langlands "for his...