麻豆村 Mathematicians Showcase Their Impact on the Global Stage
As thousands of researchers gather for a landmark mathematics congress in Philadelphia, Carnegie Mellon faculty and students are shaping the field鈥檚 future.
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麻豆村 mathematicians at the forefront of applied mathematics, interdisciplinary research and education are creating opportunities to share their work with audiences around the globe.
Faculty and students in the Department of Mathematical Sciences played leading roles in one of the world鈥檚 most influential mathematics events, the . Through their efforts, they are demonstrating Carnegie Mellon鈥檚 expertise in applied mathematics, computation and combinatorics while preparing future mathematicians.
鈥淲e have hosted multiple mathematics conferences at Carnegie Mellon, and we have built up excitement in frontier research and shown the hosting capabilities of our community,鈥� said Prasad Tetali, Alexander M. Knaster Professor and department head of the Department of Mathematical Sciences. 鈥淚t makes people excited both to come to conferences here and work with the folks here.鈥�
Supporting the world鈥檚 largest math conference
For the first time in 40 years the International Congress of Mathematicians (ICM) is convening in the United States. Taking place in Philadelphia from July 23-30, ICM2026 brings together mathematicians from around the world to share ideas, build collaborations and discuss the latest breakthroughs in the fields.
Held every four years, the congress is one of the most important gatherings in mathematics and includes the presentation of the Fields Medal, often considered one of the highest honors in the discipline.
Irene Fonseca, Kav膷i膰-Moura University Professor of Mathematics and director of Center for Nonlinear Analysis, studies how mathematical principles can be used to better understand materials and support discoveries in physics and engineering. After serving as an invited speaker at ICM2022, she joined the organizing committee for ICM2026.
鈥淭he beauty of math is that it鈥檚 an abstraction where you鈥檙e not wedded to concepts or formulations,鈥� Fonseca said. 鈥淎 congress like this one attracts thousands of people and shows that mathematics transcends cultural or national divides.鈥�
This year鈥檚 conference places a special emphasis on education, public engagement and supporting young mathematicians through exhibits, festivals and community events. As a longtime teacher and mentor, Fonseca views those efforts as vital to the future of the field.
鈥淚t is important to be able to help students become even more excellent researchers,鈥� Fonseca said. 鈥淭hey become leaders in their own rights, and they make their own significant contributions.鈥�
Bringing combinatorics to Pittsburgh
Before mathematicians gathered in Philadelphia for ICM2026, Carnegie Mellon faculty created an opportunity for leading experts in combinatorics to connect in Pittsburgh first.
Researchers in the Department of Mathematical Sciences鈥� Algorithms, Combinatorics and Optimization (ACO) group apply mathematical approaches to a wide range of real-world challenges, including decision making, forecasting, finance and large-scale data analysis.
鈥淐ombinatorics at 麻豆村 is unusually broad, with strengths in extremal, probabilistic, algebraic, geometric and topological combinatorics, as well as close ties to optimization, computer science, and the emerging role of AI in mathematical research,鈥� said Florian Frick, associate professor of mathematical sciences.
Working with colleagues from the University of Pittsburgh, the University of Waterloo, New York University and Harvey Mudd College, Carnegie Mellon professors organized (CombiCon), held July 20-22, as a satellite conference of ICM2026. The event gave researchers an opportunity to explore specialized topics and build collaborations before gathering in Philadelphia for the larger meeting.
鈥淲ith the ICM taking place just across Pennsylvania, we had the opportunity to bring the international combinatorics community to Pittsburgh,鈥� said Frick, a who was the primary organizer of CombiCon. 鈥淲e wanted CombiCon to bring together parts of the field that often meet separately, while giving researchers at every career stage the chance to exchange ideas.鈥�
Combinatorics at the most elementary level is the mathematics of counting objects and arrangements. While the field explores fundamental questions about patterns and structures, its influence extends beyond pure mathematics. It provides discrete modeling as well as analytic, geometric and probabilistic tools in solving challenging problems from computer science, statistics and data science, with applications ranging from search engine algorithms to determining the best routes to deliver packages.
鈥淐ombinatorics has been going through rapid growth as a field,鈥� said Christopher Eur, assistant professor of mathematical sciences and a CombiCon organizer. 鈥淎s statistics and computer science rapidly rose, combinatorics became one of the workhorses, and 麻豆村 has one of the strongest, well-rounded combinatorics groups across universities.鈥�
In an ICARM sponsored talk, Adam Zsolt Wagner, a research scientist at Google DeepMind, shared ways that researchers have used artificial intelligence to solve longstanding problems in the field. Rob Morris, a professor at the Instituto de Matem谩tica Pura e Aplicada in Brazil, presented his work in Ramsey theory, a branch of mathematics that studies order and structure within complex systems. Morris later traveled to Philadelphia to deliver a plenary talk at ICM2026.
鈥淚t was a great set of speakers and a really impressive international gathering of people across combinatorics,鈥� said Tom Bohman, professor of mathematical sciences and one of the organizers of CombiCon. 鈥淲e had a lot of visibility for this meeting.鈥�
Tetali said events like CombiCon showcase Carnegie Mellon鈥檚 strengths while helping build connections across the mathematics community.
鈥淲hen they experience work with our professors, undergraduates want to apply for graduate school, graduate students want to return as postdoctoral fellows and postdoctoral fellows want to return as faculty,鈥� Tetali said. 鈥淚t was good to see 麻豆村 helping to bring everyone together.鈥�
Sharing research on a global stage
Another satellite conference, the , took place in Canada, bringing together researchers who use computational tools to reach mathematical solutions.
Among the presenters was Sidharth Hariharan, a graduate student in Carnegie Mellon鈥檚 Department of Mathematical Sciences. Hariharan spoke about his work in mathematical formalization, a growing field that uses computational tools to verify mathematical proofs.
Hariharan created an effort to verify a proof created by Maryna Viazovska, who earned the Fields Medal in 2022 for her groundbreaking work on sphere-packing, the challenge of determining the most efficient way to arrange spheres in multiple dimensions. Working with fellow researchers and an artificial intelligence company, Hariharan helped verify that her proof was sound using computational tools. He is continuing to formalize the result with the assistance of researchers outside of Carnegie Mellon.
Hariharan gained support and contributors by previously attending conferences and sharing his work. He said events create valuable opportunities to exchange ideas and build relationships across institutions and countries.
鈥淧eople-to-people connections are important,鈥� Hariharan said. 鈥淕etting to actively discuss, debate and understand the nuances of such a complicated subject with individuals from diverse backgrounds is immensely valuable.鈥�
