# MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmark

arXiv: https://arxiv.org/abs/2405.12209 · HTML: https://mlsanity.com/paper/2405.12209/

## Key facts

- Cited by 105 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 20 May 2024.

## Builds on (most cited first, 20 of 20)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [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)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [Baichuan 2: Open Large-scale Language Models](https://mlsanity.com/paper/2309.10305/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Tasks](https://mlsanity.com/paper/2204.05660/) (2022)
- [Annotating Derivations: A New Evaluation Strategy and Dataset for Algebra Word Problems](https://mlsanity.com/paper/1609.07197/) (2016)

## Built on by (most cited first, 30 of 105)

- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [SDAR: A Synergistic Diffusion-AutoRegression Paradigm for Scalable Sequence Generation](https://mlsanity.com/paper/2510.06303/) (2025)
- [Are Your LLMs Capable of Stable Reasoning?](https://mlsanity.com/paper/2412.13147/) (2024)
- [Efficient Inference for Large Reasoning Models: A Survey](https://mlsanity.com/paper/2503.23077/) (2025)
- [MixLLM: Dynamic Routing in Mixed Large Language Models](https://mlsanity.com/paper/2502.18482/) (2025)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [Is Your Model Really A Good Math Reasoner? Evaluating Mathematical Reasoning with Checklist](https://mlsanity.com/paper/2407.08733/) (2024)
- [UGPhysics: A Comprehensive Benchmark for Undergraduate Physics Reasoning with Large Language Models](https://mlsanity.com/paper/2502.00334/) (2025)
- [Towards Greater Leverage: Scaling Laws for Efficient Mixture-of-Experts Language Models](https://mlsanity.com/paper/2507.17702/) (2025)
- [The Avengers: A Simple Recipe for Uniting Smaller Language Models to Challenge Proprietary Giants](https://mlsanity.com/paper/2505.19797/) (2025)
- [LLMRouterBench: A Massive Benchmark and Unified Framework for LLM Routing](https://mlsanity.com/paper/2601.07206/) (2026)
- [ErrorRadar: Benchmarking Complex Mathematical Reasoning of Multimodal Large Language Models Via Error Detection](https://mlsanity.com/paper/2410.04509/) (2024)
- [RAG-DDR: Optimizing Retrieval-Augmented Generation Using Differentiable Data Rewards](https://mlsanity.com/paper/2410.13509/) (2024)
- [HARDMath: A Benchmark Dataset for Challenging Problems in Applied Mathematics](https://mlsanity.com/paper/2410.09988/) (2024)
- [MV-MATH: Evaluating Multimodal Math Reasoning in Multi-Visual Contexts](https://mlsanity.com/paper/2502.20808/) (2025)
- [SCP-116K: A High-Quality Problem-Solution Dataset and a Generalized Pipeline for Automated Extraction in the Higher Education Science Domain](https://mlsanity.com/paper/2501.15587/) (2025)
- [Physics: Benchmarking Foundation Models on University-Level Physics Problem Solving](https://mlsanity.com/paper/2503.21821/) (2025)
- [Benchmarking Reasoning Robustness in Large Language Models](https://mlsanity.com/paper/2503.04550/) (2025)
- [WSM: Decay-Free Learning Rate Schedule via Checkpoint Merging for LLM Pre-training](https://mlsanity.com/paper/2507.17634/) (2025)
- [BoostStep: Boosting mathematical capability of Large Language Models via improved single-step reasoning](https://mlsanity.com/paper/2501.03226/) (2025)
- [Do We Truly Need So Many Samples? Multi-LLM Repeated Sampling Efficiently Scales Test-Time Compute](https://mlsanity.com/paper/2504.00762/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [SOTOPIA-Omega: Dynamic Strategy Injection Learning and Social Instruction Following Evaluation for Social Agents](https://mlsanity.com/paper/2502.15538/) (2025)
- [SciHorizon: Benchmarking AI-for-Science Readiness from Scientific Data to Large Language Models](https://mlsanity.com/paper/2503.13503/) (2025)
- [Potemkin Understanding in Large Language Models](https://mlsanity.com/paper/2506.21521/) (2025)
- [Exposing Numeracy Gaps: A Benchmark to Evaluate Fundamental Numerical Abilities in Large Language Models](https://mlsanity.com/paper/2502.11075/) (2025)
- [Exposing the Achilles' Heel: Evaluating LLMs Ability to Handle Mistakes in Mathematical Reasoning](https://mlsanity.com/paper/2406.10834/) (2024)
- [Do LLMs Understand Ambiguity in Text? A Case Study in Open-world Question Answering](https://mlsanity.com/paper/2411.12395/) (2024)
- [UGMathBench: A Diverse and Dynamic Benchmark for Undergraduate-Level Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2501.13766/) (2025)

## Abstract (arXiv)

Recent advancements in large language models (LLMs) have showcased significant improvements in mathematics. However, traditional math benchmarks like GSM8k offer a unidimensional perspective, falling short in providing a holistic assessment of the LLMs' math capabilities. To address this gap, we introduce MathBench, a new benchmark that rigorously assesses the mathematical capabilities of large language models. MathBench spans a wide range of mathematical disciplines, offering a detailed evaluation of both theoretical understanding and practical problem-solving skills. The benchmark progresses through five distinct stages, from basic arithmetic to college mathematics, and is structured to evaluate models at various depths of knowledge. Each stage includes theoretical questions and application problems, allowing us to measure a model's mathematical proficiency and its ability to apply concepts in practical scenarios. MathBench aims to enhance the evaluation of LLMs' mathematical abilities, providing a nuanced view of their knowledge understanding levels and problem solving skills in a bilingual context. The project is released at https://github.com/open-compass/MathBench .