Mathematicians judge proofs by more than their validity: simplicity, purity, and the computational cost of finding them all matter. Yet LLM-powered theorem provers have largely been built to find any correct proof, treating all valid derivations as equally acceptable. A new arXiv paper introduces LEVER, an adaptive cost-aware proof search over AND/OR graphs, as a step toward closing that gap.
The abstract frames LEVER as a response to the mismatch between mathematical practice and current automated proving. By making the search cost-aware, the method appears intended to weigh the expense of exploring different proof branches, rather than committing to a single notion of success. The 'adaptive' component suggests the search can adjust its strategy as it gathers information, though the abstract does not detail the underlying mechanism.
If LEVER works as described, it could push theorem provers toward proofs that are not only correct but also more aligned with what mathematicians actually want. The paper is at an early stage—the abstract is truncated—so the full algorithm and experimental results remain to be seen.