# Large Language Models for Mathematical Reasoning: Progresses and Challenges

arXiv: https://arxiv.org/abs/2402.00157 · HTML: https://mlsanity.com/paper/2402.00157/

## Key facts

- Cited by 284 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 67 of its 94 references that are in the map.
- First posted on arXiv 31 Jan 2024.

## Placed in

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

## Builds on (most cited first, 30 of 67)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (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)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)

## Built on by (most cited first, 30 of 284)

- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [EvolveR: Self-Evolving LLM Agents through an Experience-Driven Lifecycle](https://mlsanity.com/paper/2510.16079/) (2025)
- [LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!](https://mlsanity.com/paper/2502.07374/) (2025)
- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [Q*: Improving Multi-step Reasoning for LLMs with Deliberative Planning](https://mlsanity.com/paper/2406.14283/) (2024)
- [A Survey on Self-Evolution of Large Language Models](https://mlsanity.com/paper/2404.14387/) (2024)
- [LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning](https://mlsanity.com/paper/2410.02884/) (2024)
- [Test of Time: A Benchmark for Evaluating LLMs on Temporal Reasoning](https://mlsanity.com/paper/2406.09170/) (2024)
- [Beyond Accuracy: Evaluating the Reasoning Behavior of Large Language Models -- A Survey](https://mlsanity.com/paper/2404.01869/) (2024)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline](https://mlsanity.com/paper/2507.15855/) (2025)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [SEAL: Steerable Reasoning Calibration of Large Language Models for Free](https://mlsanity.com/paper/2504.07986/) (2025)
- [Retrieval Augmented Generation (RAG) and Beyond: A Comprehensive Survey on How to Make your LLMs use External Data More Wisely](https://mlsanity.com/paper/2409.14924/) (2024)
- [Missing Premise exacerbates Overthinking: Are Reasoning Models losing Critical Thinking Skill?](https://mlsanity.com/paper/2504.06514/) (2025)
- [Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTS](https://mlsanity.com/paper/2411.18478/) (2024)
- [What's Wrong with Your Code Generated by Large Language Models? An Extensive Study](https://mlsanity.com/paper/2407.06153/) (2024)
- [EvoCUA: Evolving Computer Use Agents via Learning from Scalable Synthetic Experience](https://mlsanity.com/paper/2601.15876/) (2026)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [FLEX: Continuous Agent Evolution via Forward Learning from Experience](https://mlsanity.com/paper/2511.06449/) (2025)
- [Astra: A Multi-Agent System for GPU Kernel Performance Optimization](https://mlsanity.com/paper/2509.07506/) (2025)
- [Parameter-Efficient Fine-Tuning in Large Models: A Survey of Methodologies](https://mlsanity.com/paper/2410.19878/) (2024)
- [RL Tango: Reinforcing Generator and Verifier Together for Language Reasoning](https://mlsanity.com/paper/2505.15034/) (2025)
- [ErrorRadar: Benchmarking Complex Mathematical Reasoning of Multimodal Large Language Models Via Error Detection](https://mlsanity.com/paper/2410.04509/) (2024)
- [A Survey of Scientific Large Language Models: From Data Foundations to Agent Frontiers](https://mlsanity.com/paper/2508.21148/) (2025)

## Abstract (arXiv)

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.