This is a joint project between Math+ and Data+. The Data+ page for this project, including posters and videos, is here.
Project leader: Professor Fan Wei
Project manager: Raymond Sun
Team members: Yasir Alhasaniyyah, Iurii Beliaev, Thomas Kidane, Kate Newbold, Robert Sun, Kevin Wang
Our research leverages cutting-edge machine learning and computational search techniques to tackle long-standing open problems in mathematics. By reframing abstract conjectures as optimization or search tasks, we use AI to explore vast possibility spaces and hunt for elusive counterexamples—specific instances that would disprove a long-held belief.
Through the development of an efficient AMCS search framework, we contributed new approaches and evidence relevant to the Sidorenko Conjecture, the Second Neighborhood Conjecture, and the universal existence of envy-free up to any item (EFX) allocations. Our methods and tools, such as a homomorphism counting library, are broadly applicable and hold promise for addressing other challenging problems in combinatorics.
The final project report can be downloaded here.