LLM framework hunts major math conjectures, passes Lean 4 checks 20/20

A new paper from researchers Alizer Wong, Zixin Zeng, and colleagues describes an LLM framework designed to systematically discover major mathematical conjectures. The system uses a three-stage pipeline: first, region search pulls explicit local evidence modules to propose candidate statements; second, reflective validation filters for foundationality, novelty, and potential significance; third, formal validation uses Lean 4 and Mathlib to verify the statements. The team's objective is to generate mathematical problems with high 'problem taste' — problems whose proofs could reorganize the language of an entire research area and provide lasting value to human mathematicians.

In experiments across twenty candidates, the pipeline showed remarkable stability. All twenty candidates passed Lean parsing and type checking, none were absorbed by the exact? tactic, and none were automatically discharged by aesop. Additionally, the system produced no explicit duplicates or near-duplicates. While passing these formal checks does not guarantee the conjectures are true or significant, the framework demonstrates a reliable path from natural-language mathematical ideas to formally verified statements. This could accelerate the discovery of new conjectures that humans might miss, potentially helping mathematicians identify promising research directions far more quickly than intuition alone.