AdvancedMathBench: A Benchmark Suite for Advanced Mathematical Proof Generation and Verification

2026-07-13

AI Summary

Existing benchmarks inadequately assess the fine-grained capabilities of large language models in generating and verifying advanced mathematical proofs. To address this gap, this work introduces a comprehensive evaluation framework spanning undergraduate to doctoral qualifying exam levels, comprising the proof generation benchmark ProverBench and the verification benchmark VerifierBench. We propose a dual-dimensional approach that integrates fine-grained error analysis with the evaluation of justification quality in verification. Leveraging large-scale expert-annotated data, we train an automated verification model capable of judging logical correctness and localizing errors, alongside constructing a high-quality human-verified dataset. Experimental results reveal that even state-of-the-art models achieve at most 75.8 (UGD) and 66.1 (QE) on generation tasks, with a best Balanced F1 score of 65.1 on verification, underscoring that advanced mathematical reasoning remains a significant challenge.

Abstract

Large language models (LLMs) have achieved remarkable performance on high-school and olympiad-style mathematics, yet their capabilities on advanced mathematics remain poorly understood. Existing benchmarks, however, fall short in both scope and evaluation granularity: they provide limited disciplinary coverage and often rely on final-answer correctness or coarse judgments, leaving the validity of the reasoning process inadequately assessed. To bridge this gap, we introduce AdvancedMathBench, a benchmark suite designed to evaluate advanced mathematical reasoning capabilities. Its core proof-generation benchmark, ProverBench, contains 296 problems spanning undergraduate and doctoral qualifying-exam levels. To provide reliable evaluation of the proofs, we develop a dedicated automatic verification pipeline trained on large-scale expert annotations to produce both correctness verdicts and fine-grained assessments of proof errors, which exhibits strong agreement with human experts on held-out proof trajectories. We further introduce VerifierBench, consisting of 888 model-generated proof trajectories paired with expert ground truth, to evaluate whether models can correctly judge proof validity and provide sound verification rationales. Experiments show that AdvancedMathBench remains challenging for frontier models. On proof generation, the best-performing model, GPT-5.5-xhigh, achieves only 75.8 and 66.1 on the UGD and QE splits, respectively, indicating substantial room for improvement on advanced mathematical proof construction. On proof verification, the best model attains a Balanced F1 of only 65.1, and models generally exhibit low true negative rates, suggesting that critical error detection remains a major bottleneck.

Problem

• mathematical proof
• large language models
• benchmark
• proof verification
• advanced mathematics

Innovation

• mathematical proof generation
• proof verification
• automatic evaluation pipeline
• expert-annotated benchmark
• fine-grained error analysis