Project Yanasse Uses AI to Generate New Mathematical Proofs via Cross-Domain Strategy Transfer

Project Yanasse has unveiled a new computational technique aimed at uncovering innovative mathematical proofs by transferring proof strategies across different mathematical domains. The method evaluates the distribution of tactics across 27 major areas within Mathlib, scrutinizing 217,133 proof states to pinpoint tactics that are prevalent in one area but either rare or non-existent in another. Utilizing GPU-accelerated NP-hard analogy matching on a MacBook Air with Apple's MPS backend, the system aligns source and target proof states. An AI reasoning agent then semantically adjusts the invocation patterns of source tactics to fit target theorems instead of merely substituting symbols. In its preliminary application, strategies were transferred from Probability to Representation Theory, resulting in 4 Lean-verified proofs from 10 attempts (a 40% success rate). All proofs compiled without "sorry" declarations, confirming their verification. This research highlights the effective transfer of tactic patterns across mathematical fields through semantic adaptation, indicating the potential to enhance mathematical discovery via cross-domain strategy transfer. This methodology marks a notable progress in automated theorem proving by utilizing structural similarities between diverse mathematical areas.