# Mathematical Language Models: A Survey

arXiv: https://arxiv.org/abs/2312.07622 · HTML: https://mlsanity.com/paper/2312.07622/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 180 of its 276 references that are in the map.
- First posted on arXiv 12 Dec 2023.

## Builds on (most cited first, 30 of 180)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [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)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [VQA: Visual Question Answering](https://mlsanity.com/paper/1505.00468/) (2015)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)

## Built on by (most cited first, 24 of 24)

- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [Beyond Accuracy: Evaluating the Reasoning Behavior of Large Language Models -- A Survey](https://mlsanity.com/paper/2404.01869/) (2024)
- [Exploring the Limit of Outcome Reward for Learning Mathematical Reasoning](https://mlsanity.com/paper/2502.06781/) (2025)
- [Does Reasoning Introduce Bias? A Study of Social Bias Evaluation and Mitigation in LLM Reasoning](https://mlsanity.com/paper/2502.15361/) (2025)
- [Surveying the MLLM Landscape: A Meta-Review of Current Surveys](https://mlsanity.com/paper/2409.18991/) (2024)
- [A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law](https://mlsanity.com/paper/2505.02665/) (2025)
- [CMM-Math: A Chinese Multimodal Math Dataset To Evaluate and Enhance the Mathematics Reasoning of Large Multimodal Models](https://mlsanity.com/paper/2409.02834/) (2024)
- [AtomThink: Multimodal Slow Thinking with Atomic Step Reasoning](https://mlsanity.com/paper/2411.11930/) (2024)
- [LLMs Are Not Intelligent Thinkers: Introducing Mathematical Topic Tree Benchmark for Comprehensive Evaluation of LLMs](https://mlsanity.com/paper/2406.05194/) (2024)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics](https://mlsanity.com/paper/2502.14333/) (2025)
- [Benchmarking Multimodal Mathematical Reasoning with Explicit Visual Dependency](https://mlsanity.com/paper/2504.18589/) (2025)
- [Can Atomic Step Decomposition Enhance the Self-structured Reasoning of Multimodal Large Models?](https://mlsanity.com/paper/2503.06252/) (2025)
- [Fairshare Data Pricing via Data Valuation for Large Language Models](https://mlsanity.com/paper/2502.00198/) (2025)
- [Evaluation of LLMs for mathematical problem solving](https://mlsanity.com/paper/2506.00309/) (2025)
- [InsertRank: LLMs can reason over BM25 scores to Improve Listwise Reranking](https://mlsanity.com/paper/2506.14086/) (2025)
- [Explain with Visual Keypoints Like a Real Mentor! A Benchmark for Multimodal Solution Explanation](https://mlsanity.com/paper/2504.03197/) (2025)
- [Teaching LLMs for Step-Level Automatic Math Correction via Reinforcement Learning](https://mlsanity.com/paper/2503.18432/) (2025)
- [Adaptive and Resource-efficient Agentic AI Systems for Mobile and Embedded Devices: A Survey](https://mlsanity.com/paper/2510.00078/) (2025)
- [Adaptive Robust Estimator for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2603.21574/) (2026)
- [MAMUT: A Novel Framework for Modifying Mathematical Formulas for the Generation of Specialized Datasets for Language Model Training](https://mlsanity.com/paper/2502.20855/) (2025)
- [Teaching LLMs to Think Mathematically: A Critical Study of Decision-Making via Optimization](https://mlsanity.com/paper/2508.18091/) (2025)
- [Reforming the Mechanism: Editing Reasoning Patterns in LLMs with Circuit Reshaping](https://mlsanity.com/paper/2603.06923/) (2026)
- [Large Language Models for Math Education in Low-Resource Languages: A Study in Sinhala and Tamil](https://mlsanity.com/paper/2602.14517/) (2026)

## Abstract (arXiv)

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a comprehensive survey of mathematical LMs, systematically categorizing pivotal research endeavors from two distinct perspectives: tasks and methodologies. The landscape reveals a large number of proposed mathematical LLMs, which are further delineated into instruction learning, tool-based methods, fundamental CoT techniques, advanced CoT methodologies and multi-modal methods. To comprehend the benefits of mathematical LMs more thoroughly, we carry out an in-depth contrast of their characteristics and performance. In addition, our survey entails the compilation of over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. Addressing the primary challenges and delineating future trajectories within the field of mathematical LMs, this survey is poised to facilitate and inspire future innovation among researchers invested in advancing this domain.