Proof Perplexity: A Probabilistic Approach to Measuring non-triviality in Machine Generated Proofs

In this article, we propose a benchmark to quantify the non-triviality and novelty of machine-generated mathematical proofs compared to existing literature. Our core methodology uses a probabilistic measure to evaluate the non-triviality of the underlying mathematical arguments in comparison to the current $\mathtt{\text{MATHLIB}}$ library. Finally, we apply this benchmark to the recent proof generated by Claude on the complex zeros of the Riemann zeta function to test for non-trivial steps.