# Is Your Model Really A Good Math Reasoner? Evaluating Mathematical Reasoning with Checklist

arXiv: https://arxiv.org/abs/2407.08733 · HTML: https://mlsanity.com/paper/2407.08733/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 66 of its 80 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 66)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [InternVL: Scaling up Vision Foundation Models and Aligning for Generic Visual-Linguistic Tasks](https://mlsanity.com/paper/2312.14238/) (2023)
- [VQA: Visual Question Answering](https://mlsanity.com/paper/1505.00468/) (2015)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [OK-VQA: A Visual Question Answering Benchmark Requiring External Knowledge](https://mlsanity.com/paper/1906.00067/) (2019)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [The Dawn of LMMs: Preliminary Explorations with GPT-4V(ision)](https://mlsanity.com/paper/2309.17421/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)

## Built on by (most cited first, 30 of 48)

- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [AbstentionBench: Reasoning LLMs Fail on Unanswerable Questions](https://mlsanity.com/paper/2506.09038/) (2025)
- [PRMBench: A Fine-grained and Challenging Benchmark for Process-Level Reward Models](https://mlsanity.com/paper/2501.03124/) (2025)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [A Survey on Benchmarks of Multimodal Large Language Models](https://mlsanity.com/paper/2408.08632/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [A Survey on Evaluation of Multimodal Large Language Models](https://mlsanity.com/paper/2408.15769/) (2024)
- [CompassVerifier: A Unified and Robust Verifier for LLMs Evaluation and Outcome Reward](https://mlsanity.com/paper/2508.03686/) (2025)
- [MM-Verify: Enhancing Multimodal Reasoning with Chain-of-Thought Verification](https://mlsanity.com/paper/2502.13383/) (2025)
- [RocketEval: Efficient Automated LLM Evaluation via Grading Checklist](https://mlsanity.com/paper/2503.05142/) (2025)
- [ErrorRadar: Benchmarking Complex Mathematical Reasoning of Multimodal Large Language Models Via Error Detection](https://mlsanity.com/paper/2410.04509/) (2024)
- [AgentProcessBench: Diagnosing Step-Level Process Quality in Tool-Using Agents](https://mlsanity.com/paper/2603.14465/) (2026)
- [A Survey on Multimodal Benchmarks: In the Era of Large AI Models](https://mlsanity.com/paper/2409.18142/) (2024)
- [From Perception to Cognition: A Survey of Vision-Language Interactive Reasoning in Multimodal Large Language Models](https://mlsanity.com/paper/2509.25373/) (2025)
- [Brains vs. Bytes: Evaluating LLM Proficiency in Olympiad Mathematics](https://mlsanity.com/paper/2504.01995/) (2025)
- [AURORA:Automated Training Framework of Universal Process Reward Models via Ensemble Prompting and Reverse Verification](https://mlsanity.com/paper/2502.11520/) (2025)
- [VLRMBench: A Comprehensive and Challenging Benchmark for Vision-Language Reward Models](https://mlsanity.com/paper/2503.07478/) (2025)
- [Sailing by the Stars: A Survey on Reward Models and Learning Strategies for Learning from Rewards](https://mlsanity.com/paper/2505.02686/) (2025)
- [MPBench: A Comprehensive Multimodal Reasoning Benchmark for Process Errors Identification](https://mlsanity.com/paper/2503.12505/) (2025)
- [TreeCut: A Synthetic Unanswerable Math Word Problem Dataset for LLM Hallucination Evaluation](https://mlsanity.com/paper/2502.13442/) (2025)
- [Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning](https://mlsanity.com/paper/2412.15184/) (2024)
- [Can Vision-Language Models Evaluate Handwritten Math?](https://mlsanity.com/paper/2501.07244/) (2025)
- [Error Classification of Large Language Models on Math Word Problems: A Dynamically Adaptive Framework](https://mlsanity.com/paper/2501.15581/) (2025)
- [Temporal Consistency for LLM Reasoning Process Error Identification](https://mlsanity.com/paper/2503.14495/) (2025)
- [MathFlow: Enhancing the Perceptual Flow of MLLMs for Visual Mathematical Problems](https://mlsanity.com/paper/2503.16549/) (2025)
- [ORGEval: Graph-Theoretic Evaluation of LLMs in Optimization Modeling](https://mlsanity.com/paper/2510.27610/) (2025)
- [UTMath: Math Evaluation with Unit Test via Reasoning-to-Coding Thoughts](https://mlsanity.com/paper/2411.07240/) (2024)
- [Evaluating Mathematical Reasoning Across Large Language Models: A Fine-Grained Approach](https://mlsanity.com/paper/2503.10573/) (2025)
- [MathDebugger: Detecting and Diagnosing Errors in Synthetic Mathematical Data](https://mlsanity.com/paper/2502.19058/) (2025)
- [ProJudge: A Multi-Modal Multi-Discipline Benchmark and Instruction-Tuning Dataset for MLLM-based Process Judges](https://mlsanity.com/paper/2503.06553/) (2025)

## Abstract (arXiv)

Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user experience in real-world scenarios, has emerged as a critical issue. Current benchmarks predominantly concentrate on problem-solving capabilities, presenting a substantial risk of model overfitting and fails to accurately measure the genuine mathematical reasoning abilities. In this paper, we argue that if a model really understands a problem, it should be robustly applied across a diverse array of tasks. To this end, we introduce MathCheck, a well-designed checklist for testing task generalization and reasoning robustness, as well as an automatic tool to generate checklists efficiently. MathCheck includes multiple mathematical reasoning tasks and robustness tests to facilitate a comprehensive evaluation of both mathematical reasoning ability and behavior testing. Utilizing MathCheck, we develop MathCheck-GSM and MathCheck-GEO to assess math textual reasoning and multi-modal reasoning abilities, respectively, serving as upgraded versions of benchmarks including GSM8k, GeoQA, UniGeo, and Geometry3K. We adopt MathCheck-GSM and MathCheck-GEO to evaluate 26 LLMs and 17 MLLMs. Our results demonstrate that while frontier LLMs like GPT-4o continue to excel in various abilities on the checklist, many other model families exhibit a significant decline. Further experiments indicate that, compared to traditional math benchmarks, MathCheck better reflects true mathematical abilities and represents mathematical intelligence more linearly, thereby supporting our design. Using MathCheck, we can efficiently conduct informative behavior analysis to deeply investigate models. Finally, we show that our checklist paradigm can easily extend to other reasoning tasks.