At the beginning of this year, I went to the Joint Mathematics Meetings, JMM 2025. JMM is the largest annual meeting of mathematicians worldwide. Each year, JMM has a special theme, and this year, it was "We Decide Our Future: Mathematics in the Age of AI." That means that in addition to all the regular sessions where talks are given on various mathematical topics, special thematic talks and sessions on AI were also included.
I was privileged to have been invited to give two talks. My first talk was a regular short talk on a result related to combinatorics and machine learning. My second talk was an hour-long talk for a more general audience in a special session called "AI for the Working Mathematician." The main organizer of the special session was Akshay Venkatesh, a Fields medalist in number theory. He's not an AI researcher, but he's thinking about these issues along with many others.
This second talk of mine got a lot of enthusiastic feedback in the form of follow-up emails and discussions, so I want to write down some of my thoughts from that talk. A link to the talk slides is here. The short summary is:
- We are already at the point where machine learning is already useful for research mathematics, both as structured systems (e.g. Copilot Lean) and as general LLMs (e.g. GPT-o1) -- I gave examples of both.
- In most cases, the time period between when machine learning starts to be able to do tasks and when it overtakes humans is usually short, so we should enjoy the current "golden age of mathematics," which has already begun.
- The claim that math is inherently different from other endeavors where AI has taken over isn't well supported. We begin with ZF/C (start position) and need to arrive at a theorem (winning position) using logical deductions (legal moves). How is this fundamentally different from chess? (This is related to an observation made by Matus Telgarsky in his excellent talk.)
- We are very far behind in understanding Deep Learning, and we will remain so for cutting-edge systems. Perhaps one hope of catching up is if we use AI systems to help ourselves understand them.
- There is still a role for mathematicians to play in advancing the state of the art: machine learning reductions come to mind as one place where we can still make theoretical advances that are useful.