# A Survey on Large Language Models for Mathematical Reasoning

arXiv: https://arxiv.org/abs/2506.08446 · HTML: https://mlsanity.com/paper/2506.08446/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 193 of its 246 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Placed in

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

## Builds on (most cited first, 30 of 193)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [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)
- [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)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [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)
- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)

## Built on by (most cited first, 30 of 52)

- [Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline](https://mlsanity.com/paper/2507.15855/) (2025)
- [VCRL: Variance-based Curriculum Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2509.19803/) (2025)
- [Knapsack RL: Unlocking Exploration of LLMs via Optimizing Budget Allocation](https://mlsanity.com/paper/2509.25849/) (2025)
- [AgentArk: Distilling Multi-Agent Intelligence into a Single LLM Agent](https://mlsanity.com/paper/2602.03955/) (2026)
- [Supervised Reinforcement Learning: From Expert Trajectories to Step-wise Reasoning](https://mlsanity.com/paper/2510.25992/) (2025)
- [Towards Natural Personalization: Evaluating Long-Horizon Preference Following in Personalized User-LLM Interactions](https://mlsanity.com/paper/2603.04191/) (2026)
- [Token-Level LLM Collaboration via FusionRoute](https://mlsanity.com/paper/2601.05106/) (2026)
- [Uncertainty-Aware Clarification in LLM Agents with Information Gain](https://mlsanity.com/paper/2606.03135/) (2026)
- [Thinking Longer, Not Always Smarter: Evaluating LLM Capabilities in Hierarchical Legal Reasoning](https://mlsanity.com/paper/2510.08710/) (2025)
- [RSPO: Risk-Seeking Policy Optimization for Pass@k and Max@k Metrics in Large Language Models](https://mlsanity.com/paper/2508.01174/) (2025)
- [Teaching Language Models to Reason with Tools](https://mlsanity.com/paper/2510.20342/) (2025)
- [LawThinker: A Deep Research Legal Agent in Dynamic Environments](https://mlsanity.com/paper/2602.12056/) (2026)
- [Learning from Your Own Mistakes: Constructing Learnable Micro-Reflective Trajectories for Self-Distillation](https://mlsanity.com/paper/2606.18844/) (2026)
- [SP-Mind: An Autonomous Reasoning Agent for Spatial Proteomics Analysis](https://mlsanity.com/paper/2606.24235/) (2026)
- [FormalRx: Rectify and eXamine Semantic Failures in Autoformalization](https://mlsanity.com/paper/2607.04655/) (2026)
- [AgentCoMa: A Compositional Benchmark Mixing Commonsense and Mathematical Reasoning in Real-World Scenarios](https://mlsanity.com/paper/2508.19988/) (2025)
- [PISA-Bench: The PISA Index as a Multilingual and Multimodal Metric for the Evaluation of Vision-Language Models](https://mlsanity.com/paper/2510.24792/) (2025)
- ["To Survive, I Must Defect": Jailbreaking LLMs via the Game-Theory Scenarios](https://mlsanity.com/paper/2511.16278/) (2025)
- [Self-Supervised Bootstrapping of Action-Predictive Embodied Reasoning](https://mlsanity.com/paper/2602.08167/) (2026)
- [Agentic Game Development as a Verifiable Trajectory Data Engine for Scaling World Models](https://mlsanity.com/paper/2608.25518/) (2026)
- [MMR-GRPO: Accelerating GRPO-Style Training through Diversity-Aware Reward Reweighting](https://mlsanity.com/paper/2601.09085/) (2026)
- [Adaptive Robust Estimator for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2603.21574/) (2026)
- [Neuron-Anchored Rule Extraction for Large Language Models via Contrastive Hierarchical Ablation](https://mlsanity.com/paper/2605.03058/) (2026)
- [RAG over Thinking Traces Can Improve Reasoning Tasks](https://mlsanity.com/paper/2605.03344/) (2026)
- [Single-Rollout Hidden-State Dynamics for Training-Free RLVR Data Selection](https://mlsanity.com/paper/2605.28631/) (2026)
- [Harnessing Routing Foresight for Micro-step-level MoE load balancing in RL Post-training](https://mlsanity.com/paper/2606.11867/) (2026)
- [Efficient Test-Time Optimization for Multi-Agent Proof Autoformalization](https://mlsanity.com/paper/2607.11307/) (2026)
- [Proof2Hybrid: Automatic Mathematical Benchmark Synthesis for Proof-Centric Problems](https://mlsanity.com/paper/2508.02208/) (2025)
- [Beyond Token-level Supervision: Unlocking the Potential of Decoding-based Regression via Reinforcement Learning](https://mlsanity.com/paper/2512.06533/) (2025)
- [Constructive Circuit Amplification: Improving Math Reasoning in LLMs via Targeted Sub-Network Updates](https://mlsanity.com/paper/2512.16914/) (2025)

## Abstract (arXiv)

Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.