(Fun)damental Uses of AI in Math: Research
How can AI be useful in mathematical research and how might this change the nature of that research?
These questions have been brought into focus in the past year due to advances in LLMs, formalization/autoformalization, and more customized AI toolboxes. This event will be a chance to hear perspective on these tools and questions from mathematicians working on the cutting edge of AI in math research, and to get a glimpse at what the future may hold.
This event was part of the Frontiers in Data Science and AI initiative at the Data Science Institute, Columbia University.
Event Details
Thursday, February 5, 2026 (1:00 PM - 6:00 PM ET)
Davis Auditorium, CEPSR (4th Floor - Campus Level) - Campus Map
Speakers & Talk Information
Rajesh Jayaram, Research Scientist, Google Research NYC
Leveraging Inference Scaling for Mathematical Problem Solving and Verification
Abstract: Last year witnessed tremendous improvements in the reasoning capabilities of Large Language Models, with Gemini and GPT winning a gold medal at both the International Mathematical Olympiad (IMO) [1] and the International Collegiate Programming Contest (ICPC) [2]. In addition to their skill at problem solving, they have also proven to be proficient verifiers. In an experimental program at STOC [3], Gemini-based models found significant bugs in complex mathematical proofs, and in an ongoing program at ICML these models are being used to provide deep feedback for experimental papers as well [4].
Despite these significant advances, models still suffer from notable issues when employed in the research process. They can hallucinate facts and references, make reasoning errors, and hand-wave over critical arguments. In this talk, we will discuss the power of inference scaling techniques to significantly mitigate these issues and improve performance. By formulating the key features of the inference scaling problem as a concrete optimization task, we can begin a more principled study of how best to leverage AI to assist in mathematical research while given a limited computed budget.
Tristan Buckmaster, Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University
Fluid Singularities, Unstable PDE Solutions and Computer-assisted Proofs
Abstract: This talk presents recent work on understanding certain solutions of PDE by combining modern mathematics with classical analysis. Machine learning, particularly Physics-Informed Neural Networks (PINNs), is being applied to discover new solutions to nonlinear PDEs with high accuracy. A key aspect is the interplay between these methods to uncover the full spectrum of solutions, significantly, unstable solutions that are challenging to find otherwise.
We will also demonstrate how computer-assisted methods can transform these numerical discoveries into rigorous mathematical proofs. While motivated by fluid mechanics equations such as Euler and Navier-Stokes, the methods discussed have broader applicability to other PDEs.
Iddo Drori, Associate Professor, Department of Computer Science & Engineering, Yeshiva University
AI for Superhuman Math
Abstract: IMO 2025 saw AI achieve gold-medal level performance. Recently, AI-driven methods have proved dozens of open conjectures and Erdős problems. We present a reproducible analysis that includes cross-model grading bias, multilingual leakage testing, comparison of AI and human solution strategies, and formal proof comparisons. We verify that AI models solve all IMO 2025 problems and show that even the most difficult combinatorics problem is solved by pairing AI models with evolutionary programming.
Sergei Gukov, John D. MacArthur Professor of Theoretical Physics and Mathematics, Caltech
The role of AI in mathematical (re)search
Abstract: At its core, scientific research is a search, a search for new ideas, new patterns, and new ways to explain or prove things. In this talk, I invite you to explore how AI is reshaping different stages of this process. We will see that while AI excels at many tasks, it still hesitates on others, such as long-horizon reasoning or far-out-of-distribution generalization. I view this as good news: it highlights how much meaningful AI research remains to be done. In fact, the goal of expanding AI's role in mathematical research has become a motivation for advancing AI itself. I am genuinely excited that these two fields have come into such close contact over the past few years.
Mehtaab Sawhney, Assistant Professor of Mathematics, Arts & Sciences, Columbia University
LLMs as Research Assistants
Abstract: We will walk through a collection of examples where GPT 5 has been used to either assist mathematicians in research level tasks or where it has proven new results autonomously. The focus will be on lessons to draw for a practicing mathematician.
Agenda
Thursday, February 5, 2026
1:05 PM: Rajesh Jayaram, Research Scientist, Google Research NYC (30 min)
1:40 PM: Tristan Buckmaster, Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University (30 min)
2:10 PM: Iddo Drori, Associate Professor, Department of Computer Science & Engineering, Yeshiva University (30 min)
2:40 PM: Break (20 min)
3:00 PM: Sergei Gukov, John D. MacArthur Professor of Theoretical Physics and Mathematics, Caltech - presenting remotely (30 min)
3:30 PM: Mehtaab Sawhney, Assistant Professor of Mathematics, Arts & Sciences, Columbia University - presenting remotely (30 min)
4:00 PM - 4:15 PM: Break (15 min)
DSI Frontiers Awardees: (Fun)damental AI and Math Series
- Ivan Corwin, Professor of Mathematics and Statistics, Arts & Sciences, Columbia University
- Andrew J. Blumberg, Herbert and Florence Irving Professor of Cancer Data Research (in the Herbert and Florence Irving Institute of Cancer Dynamics and in the Herbert Irving Comprehensive Cancer Center) and Professor of Mathematics and Computer Science
- Kriste Krstovski, Associate Research Scientist, Data Science Institute
- Daniel Hsu, Associate Professor of Computer Science, Columbia Engineering
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