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The congress brought together the world’s math community while serving as a forum for discussing how new technologies such as AI and Lean are shaping the field.
The International Congress of Mathematicians (ICM) is often described as the Olympics of mathematics. Held every four years by the International Mathematical Union (IMU), the meeting brings together thousands of mathematicians from around the world to build community, present research and exchange ideas.
The 2026 ICM, held in Philadelphia this July, featured eight days of talks, workshops and opportunities for collaboration that set the stage for new discoveries and celebrated all things mathematics.
The Simons Foundation served as the leading local organizer of this year’s congress, with additional support from the American Mathematical Society. The gathering marked the first ICM held in the United States since 1986 and was an important moment of unity in a time when barriers are increasingly hindering international collaboration.
“The IMU exists to support the worldwide mathematical community,” said IMU President Hiraku Nakajima in his opening remarks to kick off the meeting. “Its mission is to promote international cooperation in mathematics to support the development of mathematics in all countries, and to help ensure that the mathematicians can meet, communicate and work together. These goals sound simple, but they are not automatic. They require effort, trust and shared commitment.”
Perhaps the most valuable part of this year’s ICM was the opportunity for mathematicians to meet experts from around the world with whom they might never otherwise cross paths. And with researchers from vastly different fields gathered under one roof, the meeting creates opportunities for unexpected connections across disciplines.
“Usually, conferences in my area are pretty small — around 50 people — and I already know 49 of them,” says attendee Sonya Farr, a postdoctoral fellow at the Max Planck Institute for Mathematics in Germany. “This is a chance to talk to people I don’t usually see. Math nowadays is about knowing two unrelated things and then seeing the connections between them, so you need exposure to those unrelated areas.”
The Simons Foundation provided travel grants that enabled mathematicians from other countries to attend the ICM, facilitating conversations and collaborations among researchers.
“I’m from Bangladesh and was only able to come here because of a Simons travel grant,” says attendee Hena Rani Biswas, an associate professor of mathematics at the University of Barishal in Bangladesh. “I’ve already met two people I want to collaborate with – one from Brazil and one from Japan. It has been an amazing experience so far.”
While mathematics may often be portrayed as a solitary pursuit, those in the field know it is distinctly the opposite.
“A question after a lecture, a chance meeting, a discussion between mathematicians from different countries and traditions may have consequences that none of us foresee,” said Jalal Shatah, co-chair of the ICM’s local organizing committee and a mathematician at New York University, in his opening ceremony remarks. “These encounters are not secondary to the Congress; they are an essential part of its purpose. The ICM represents openness, solidarity and the shared intellectual purpose.”
From auditorium-filling marquee talks to hallway conversations over coffee, the ICM serves as a crucial venue for mathematicians to discuss and debate the most important topics shaping the field. AI, for example, was a hot topic of discussion as mathematicians navigate its revolutionary impact on the field.
University of California, Los Angeles mathematician Terry Tao, a 2006 Fields Medalist, shared his thoughts in a public lecture in which he asked attendees to consider why they do mathematics and what counts as successful mathematics. Grappling with these questions, he argues, will be imperative for understanding AI’s place in the field.
“Let’s assume that soon, AI will be able to perform a reasonable fraction of mathematical tasks successfully,” he said. “If you condition for that, it becomes clear that we now have to think about our goals and our values.”
Another session centered on Lean, a proof assistant that has evolved into a “truth oracle” capable of verifying or refuting any mathematical or logical assertion. At ICM 2026, mathematics writer Kevin Hartnett spoke about his book The Proof in the Code. Published by the Simons Foundation’s Quanta Books, the book explores Lean’s development and what it could mean for how human mathematicians collaborate with AI.
“The utility of AI is that it can generate a lot of possibilities. It can explore a big space quickly, but it’s not reliable, and it’s hard to review all its suggestions,” he said. “Lean can quickly check them and tell you if they’re correct or not. That’s a virtue of it. We need systems for verification, using theorem provers, in a way we maybe didn’t feel as urgently before.”
AI isn’t the only field that mathematics touches. The ICM showcased several unexpected disciplines where mathematics plays a big role, including in sports analytics. In a panel discussion, analysts from Philadelphia’s major sports teams (the Phillies, Eagles, Union, Flyers and 76ers) described how they’ve gone from tiny one-person departments to large teams swimming in tracking data, biomechanics and even mental-performance information. The big challenge for sports analytics now, they say, is making the best use of the data rather than figuring out how to collect it.
“The data is blowing up faster than we can keep up,” said Fan-Hal Koung, the Sixers’ assistant general manager, during the panel. “In 2014, it was almost an advantage that we had limited data, because it forced us to focus research on very specific things. Now, with tracking and everything else, the hardest work isn’t technical — it’s deciding where to spend our time.”
A highlight of each ICM is the announcement of the Fields Medals winners. The Fields Medals are among the highest honors in mathematics, awarded every four years by the IMU to outstanding mathematicians under age 40. The 2026 medals went to Yu Deng of the University of Chicago, John Pardon of Princeton University and Stony Brook University, Jacob Tsimerman of the University of Toronto and Hong Wang of New York University and the Institut des Hautes Études Scientifiques in France.
Deng received the award for his groundbreaking work developing new mathematical methods to better understand how waves and other physical phenomena behave. “Roughly speaking, what I do is connect the microscopic to the macroscopic in the universe,” he says. Deng and colleagues leveraged this approach to solve a version of Hilbert’s sixth problem, a 124-year-old challenge, with a 200-page proof.
Pardon was chosen for his work creating new mathematical tools that help mathematicians better understand the shapes and structures that arise in geometry and topology. His work helped prove the 20-year-old MNOP conjecture, showing that two seemingly unrelated methods for counting curves on certain six-dimensional shapes are actually equivalent. “A resistant problem is like climbing a mountain,” he says. “It might be painful, but you have a sense of accomplishment at the top.”
Tsimerman is recognized for developing powerful new ways to use o-minimality (a concept from mathematical logic) to solve major problems in number theory and algebraic geometry. “When doing number theory, you try to understand statistically what you expect to happen, and then whenever something unexpected happens, you look for geometric explanations for it,” he explains.
Wang won the medal in part for her breakthrough work on the Kakeya conjecture, a century-old problem in geometry about how much space is needed to rotate a line segment so that it points in every possible direction. “One lesson I’ve learned through mathematics is that as long as you get something in the end, it doesn’t matter how much time it takes for you. It’s OK to take your time,” she says.
Several other prestigious awards were also announced at the ICM.
The 2026 Abacus Medal went to Shayan Oveis Gharan of the University of Washington for his work improving the efficiency of computers in solving difficult problems, including the traveling salesperson problem.
The Chern Medal went to Graeme Segal of the University of Oxford for his visionary mathematical insights, which have influenced topology, mathematical physics, representation theory and category theory.
The Carl Friedrich Gauss Prize was awarded to Yurii Nesterov of Université Catholique de Louvain in Belgium for his groundbreaking work in mathematical optimization, which has provided the theoretical foundation and algorithmic backbone for many numerical and data-driven fields.
Hannah Fry won the 2026 Leelavati Prize for bringing mathematics to millions of people through books, television and other media, making mathematical ideas engaging and relevant to everyday life.
The ICM also served as an opportunity to remember and celebrate the impact of Jim Simons, co-founder of the Simons Foundation, who died in 2024. A reception honored his contributions to the field and his support of mathematics worldwide. Funding mathematical research was a driving force behind the launch of the Simons Foundation, and integrating mathematics into different fields has long been a tenet of the foundation’s approach.
“As Galileo said, nature itself is written in the language of mathematics, and we, as a foundation, have been supporters of the ‘mathematization’ of fields like biology and neuroscience, and the use of mathematical tools across science,” said Simons Foundation President David Spergel at the event.
Marilyn Simons also reflected on Jim’s lasting impact and his curious spirit.
“I was lucky to spend my life with Jim,” she said. “Over the course of his career, he pursued many different paths, and after more than 50 years together, I can honestly say he was never boring. He was always ready to embrace new ideas and new directions. He was a wonderful leader and a wonderful husband.”
Perhaps above all, Jim believed deeply that the greatest discoveries are only possible through collaboration.
“This is why we’re so proud to be supporters of the ICM,” said Spergel. “Because it’s an opportunity to bring people together from throughout the world to have exciting and interesting conversations. That’s what Jim loved.”
