# Mathematical Reasoning in Large Language Models: Benchmarks, Architectures, Evaluation, and Open Challenges

arXiv: https://arxiv.org/abs/2605.19723 · HTML: https://mlsanity.com/paper/2605.19723/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 119 references that are in the map.
- First posted on arXiv 19 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (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)
- [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)
- [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 Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Using DeepSpeed and Megatron to Train Megatron-Turing NLG 530B, A Large-Scale Generative Language Model](https://mlsanity.com/paper/2201.11990/) (2022)
- [Detecting Pretraining Data from Large Language Models](https://mlsanity.com/paper/2310.16789/) (2023)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text](https://mlsanity.com/paper/2310.06786/) (2023)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs](https://mlsanity.com/paper/2402.14903/) (2024)
- [O1 Replication Journey -- Part 2: Surpassing O1-preview through Simple Distillation, Big Progress or Bitter Lesson?](https://mlsanity.com/paper/2411.16489/) (2024)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [Reward Shaping to Mitigate Reward Hacking in RLHF](https://mlsanity.com/paper/2502.18770/) (2025)
- [Learning from Few Examples: A Summary of Approaches to Few-Shot Learning](https://mlsanity.com/paper/2203.04291/) (2022)
- [MathBERT: A Pre-Trained Model for Mathematical Formula Understanding](https://mlsanity.com/paper/2105.00377/) (2021)
- [Toward a Theory of Tokenization in LLMs](https://mlsanity.com/paper/2404.08335/) (2024)
- [Benchmarking Reasoning Robustness in Large Language Models](https://mlsanity.com/paper/2503.04550/) (2025)
- [Autoformalization in the Wild: Assessing LLMs on Real-World Mathematical Definitions](https://mlsanity.com/paper/2502.12065/) (2025)
- [Label Supervised LLaMA Finetuning](https://mlsanity.com/paper/2310.01208/) (2023)
- [Fuse, Reason and Verify: Geometry Problem Solving with Parsed Clauses from Diagram](https://mlsanity.com/paper/2407.07327/) (2024)

## Built on by (most cited first, 1 of 1)

- [From Chatbot to Digital Colleague: The Paradigm Shift Toward Persistent Autonomous AI](https://mlsanity.com/paper/2606.14502/) (2026)

## Abstract (arXiv)

Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning capabilities, understanding how well they perform mathematical reasoning has become increasingly important. This survey synthesizes recent advancements in mathematical reasoning with LLMs through a structured analysis of datasets, architectures, training strategies, and evaluation protocols. Our systematic review encompasses approximately 120 peer-reviewed studies and preprints, examining the evolution of this research area and providing a unified analytical framework to understand current progress and limitations. Our study particularly introduces a unified taxonomy of mathematical datasets, distinguishing between pretraining corpora, supervised fine-tuning resources, and evaluation benchmarks across varying levels of reasoning complexity. A systematic analysis of reasoning architectures and training strategies, including tool integration, verifier-guided reasoning, and parameter-efficient adaptation, is presented to assess their effects on reasoning robustness and generalization. Moreover, a comparative evaluation of existing metrics highlights the gap between final-answer accuracy and process-level reasoning verification. By synthesizing insights across these areas, our analysis identifies recurring failure modes, such as reasoning faithfulness issues, benchmark biases, and generalization limitations, and outlines key research directions toward improving symbolic grounding, evaluation reliability, and the development of more robust and trustworthy LLM-based reasoning systems.