(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 is part of the Frontiers in Data Science and AI initiative at the Data Science Institute, Columbia University.

REGISTER

REGISTRATION DEADLINE: The Columbia Morningside campus is open to the Columbia community. If you do not have an active CUID, the deadline to register is at 12:00 PM the day before the event.

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Event Details & Agenda

Thursday, February 5, 2026 (1:00 PM – 6:00 PM ET)

Location: Davis Auditorium (CEPSR) – 4th Floor (Campus Level)
Address: 530 W 120th St, New York, NY 10027

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Details below subject to change:

1:00 PM – 1:05 PM: Introductions: Ivan Corwin, Professor of Mathematics and Statistics, Arts & Sciences, Columbia University (5 min)

Presentations:

1:05 PM – 1:35 PM: Rajesh Jayaram, Research Scientist, Google Research NYC (30 min)

1:40 PM – 2:10 PM: Tristan Buckmaster, Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University (30 min)

2:10 PM – 2:40 PM: Iddo Drori, Associate Professor, Department of Computer Science & Engineering, Yeshiva University (30 min)

2:40 PM – 3:00 PM: Break (20 min)

3:00 PM – 3:30 PM: Sergei Gukov, John D. MacArthur Professor of Theoretical Physics and Mathematics, Caltech – presenting remotely (30 min)

3:30 PM – 4:00 PM: Mehtaab Sawhney, Assistant Professor of Mathematics, Arts & Sciences, Columbia University – presenting remotely (30 min)

4:00 PM – 4:15 PM: Break (15 min)

4:15 PM – 5:15 PM: Panel Discussion (60 min)

• Moderator: 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
• Tristan Buckmaster, Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University
• Iddo Drori, Associate Professor, Department of Computer Science & Engineering, Yeshiva University
• Michael Harris, Professor of Mathematics, Arts & Sciences, Columbia University
• Ivan Corwin, Professor of Mathematics and Statistics, Arts & Sciences, Columbia University
• Ivan Zelich, PhD Student, Mathematics, Arts & Sciences, Columbia University
• Roger van Peski, Joseph Fels Ritt Assistant Professor of Mathematics, Arts & Sciences, Columbia University

5:15 PM – 5:30 PM: Research Project Discussion: Kriste Krstovski, Associate Research Scientist, Data Science Institute (15 min)

5:30 PM – 6:00 PM: Demonstration on AI Tools: Ivan Zelich, PhD Student, Mathematics, Arts & Sciences, Columbia University (30 min)

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Speaker Details

Listed in order of program appearance:

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.

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.

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.

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.

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.

Research Project Discussion

Overview: Research into AI tools for mathematics is gaining momentum. To foster collaboration between mathematicians and AI researchers, the program will highlight recent research opportunities as illustrative examples, motivating faculty to propose ideas that can seed cross domain collaborations.

Demonstration on AI Tools

Overview: Large Language Models (LLMs) provide us with a valuable searching and generalizing ability. We will spend the first part of the session discussing how we can harness this ability for mathematical research, and the common issues that may arise when trying to do so. Afterwards, we will be prompting various LLM models with interesting and fun mathematics problems, so come armed with your own questions to put these models to the test!