Tencent's Hyra AI Agent Solves 50-Year-Old Additive Combinatorics Problem
Tencent Hunyuan announced that its scientific AI agent, Hyra, based on the Hy3 model, has solved a 50-year-old open problem in additive combinatorics. The team has published a preprint paper along with a formal verification of the proof using the Lean proof assistant. This achievement highlights the growing capability of AI agents to assist in complex mathematical discovery and formal verification. By providing a Lean-verified proof, it bridges the gap between AI-generated conjectures and mathematically rigorous, machine-checked solutions. The problem involves analyzing how much a finite integer set expands under addition (sumset A+A) versus subtraction (difference set A-A). The code for the explicit construction and the Lean formal proof has been open-sourced on GitHub.
## BACKGROUND
Additive combinatorics is a branch of mathematics that studies the structure and size of sumsets and difference sets of finite subsets in abelian groups. Lean is an open-source proof assistant and programming language widely used by mathematicians to write computer-checked, formally verified mathematical proofs.