Frontiers in pure mathematics and theoretical computer science

Leads: Vlad Vicol and Anupam Gupta

The purpose of this area is mathematical discovery: using AI systems to obtain new results in pure mathematics and theoretical computer science, on problems that Courant’s faculty consider central to their fields. AI already contributes to research of this kind: it finds constructions and counterexamples, tests conjectures, and helps write proofs. We intend to go further, and to understand what makes such results possible.

We will work with open-weight models, which we can train and eventually optimize for our desired downstream objectives, but also with the strongest publicly available closed models. We aim to build field-specific custom harnesses in which the model works: how the problem is posed, what input it is given, how a proposed answer is checked, and what is left to the mathematician. Learning which kinds of problems yield to this approach, and why, is part of the research.

The problems come from our members’ own research programs, chosen for their mathematical importance rather than their convenience. Every problem we take on also helps train our open-weight models, supplying both new data and tested workflows for doing mathematics.