Mathematicians Outperform AI in Solving a Combinatorics Problem

$Leonid Petrov, UVA Mathematics Professor$

Mathematics professor Leonid Petrov , with collaborators David Anderson (Ohio State University) and Greta Panova (University of Southern California), has resolved a 10-year-old problem in algebraic combinatorics that AI-driven approaches had failed to crack. Despite recent excitement about AI as a tool for mathematical discovery, no automated system had been able to locate a counterexample to the long-standing Merzon-Smirnov conjecture on Schubert polynomials. Petrov, Anderson, and Panova disproved the conjecture by combining sharper computational methods with new theoretical insight, finding the first counterexample at n = 17, just beyond the reach of earlier exhaustive searches.

The preprint is on the arXiv: Computation and sampling for Schubert specializations. A new UVA Arts & Sciences article highlights the result and its place in the broader conversation about AI in mathematics.

Last updated: Monday, April 27, 2026