---
title: "AdvancedMathBench：高级数学证明生成与验证基准套件"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.11849v1"
permalink: "https://feed.astralor.com/items/itm_74f28fd8f092e3f6e33cd039"
published: "2026-07-13T17:38:22.000Z"
score: 78
channel: "ai"
tags: ["AdvancedMathBench","GPT-5.5","LLM","数学推理","证明验证"]
---

# AdvancedMathBench：高级数学证明生成与验证基准套件

## AI 点评

> 这篇论文最打动我的是它对高级数学推理评估的细化——不再只看最终答案，而是深入到证明过程和错误检测。对于想要突破LLM推理极限的研究者来说，ProverBench和VerifierBench提供了宝贵的测试场。特别适合AI推理方向的研究人员和评估团队关注。

## 速览

AdvancedMathBench 基准套件包含 ProverBench（296 道本科至博士资格考试级别题目）和 VerifierBench（888 条带专家标注的模型生成证明轨迹），用于评估 LLM 在高级数学证明生成与验证上的能力。实验表明，最佳模型 GPT-5.5 在 UGD/QE 分集上的得分仅为 75.8/66.1，验证 Balanced F1 仅 65.1，且真阴性率低，说明关键错误检测仍是主要瓶颈。

## 关键点

- 提出 AdvancedMathBench 套件，包含 ProverBench 和 VerifierBench，覆盖本科至博士资格考试级别的高级数学证明。
- 开发了基于大规模专家标注的自动证明验证 pipeline，与人类专家判断高度一致。
- GPT-5.5 在证明生成上 UGD 分集 75.8，QE 分集 66.1，证明验证 Balanced F1 仅 65.1。
- 模型普遍真阴性率低，关键错误检测是当前主要瓶颈。

## 全文

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.

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