LLM Mathematical Reasoning

LLM: Large Language Model

The field investigates whether language models can carry out arithmetic, multi-step problem solving, and proof construction reliably—not just produce correct-looking answers. Common approaches include chain-of-thought prompting, supervised and reinforcement learning, test-time search and voting, tool use with code or computer algebra, and formal verification with proof assistants such as Lean. Evaluation spans word-problem and contest benchmarks such as GSM8K, MATH, and AIME, as well as formal proof tasks like miniF2F; newer tests probe robustness to equivalent transformations, multilingual inputs, and research-level problems. Models can perform strongly on familiar contest tasks, but generalization, faithful reasoning, proof quality, and reliable verification remain unresolved tensions, especially on open-ended research mathematics.

Latest papers

271 papers20 papers in the last four weeks, down 5% on the four weeks before. 0.1% of all new papers.

H $^2$ R: Hierarchical Hint-Based Reward for Mathematical Reasoning via Reinforcement Learning
Oct 29, 2026He Tu, Siye Li, Hongyi WenLLM Mathematical Reasoning Reward Shaping
New York University Shanghai
Efficient Proof Generation for Lean Statements with Multiple Candidate Answers
Oct 25, 2026Pengzhen Lin, Ke Zhang, Maziar Raissi +1Automated Theorem Proving LLM Mathematical Reasoning
University of California, Riverside
ClaimScope: Label-Blind Witness Verification for Mathematical Claim Auditing
Oct 15, 2026Mushir AkhtarLLM Mathematical Reasoning Agent Benchmarks
IneqAgent: Agentic Inequality Proving in Lean with Symbolic Computation
Oct 14, 2026Gaolei He, Jinhui Li, Ruobing Zuo +2Lean Theorem Proving LLM Mathematical Reasoning
School of Software Engineering, East China Normal University · School of Computer and Information Science, Southwest University
Attention-Graph Curvature for the Verification of Mathematical Reasoning
Oct 12, 2026Kanghyeon Kim, Johannes F. Lutzeyer, Yanzhu GuoLanguage Model Error Detection Reasoning Verification
Télécom Paris, IPP · LIX, CNRS, École Polytechnique, IPP
ACED: Reference-Anchored Aggregation of Natural-Language and Executable Evidence for Mathematical Reasoning
Oct 12, 2026Yiyi Lu, Jiaxiang Geng, Bing LuoLLM Mathematical Reasoning LLM Reasoning
1Duke Kunshan University · 2The University of Hong Kong
MathVis: Can AI Reason through Drawing? A Benchmark for Mathematical Figure Generation
Oct 9, 2026Jingjing Wei, Hao Zhao, Xinke Li +3Mathematical Reasoning Benchmarks LLM Mathematical Reasoning
Zhihu (zhihu.com) · Tsinghua University (tsinghua.edu.cn) · City University of Hong Kong (cityu.edu.hk) +1
Bolzano: From Expert-Guided Proof Search to Automated Open-Problem Solving
Oct 7, 2026Adrián Zámečník, Matěj Kripner, Martin Koutecký +5Automated Theorem Proving AI Agents for Scientific Discovery
Computer Science Institute, Charles University · Institute of Formal and Applied Linguistics, Charles University · Department of Applied Mathematics, Charles University +1
Let the Library Speak: Self-Advertised Method Selection for Formal Proving
Oct 7, 2026Xiaopeng Yuan, Suijin Wang, Yanli Wang +5Automated Theorem Proving LLM Mathematical Reasoning
University of Illinois at Urbana-Champaign · Tsinghua University · Imperial College London +1
When Tools Lie: Reliability of Mathematical Agents Under Corrupted Tool Feedback
Oct 6, 2026Kavienan Jegatheesan, Gayathri LihinikaduarachchiLLM Agent Verification LLM Agent Reliability
Dept. of Computer Science and Engineering University of Moratuwa, Sri Lanka
CALR: Continuous Anchored Latent Reasoning via Render-of-Thought Compression
Oct 5, 2026Zhaoyang Wei, Bowen Jiang, Yanchao Hao +5Efficient Language Model Reasoning Latent Visual Reasoning
University of the Chinese Academy of Sciences · Tencent
When Does Longer Reasoning Help? Predicting Mathematical Reasoning Through Discovery and Execution
Oct 4, 2026Adib Hasan, Lay Jain, Thanic Nur SaminInference-Time Scaling LLM Mathematical Reasoning
Independent Researcher · IU Bloomington
Continual Graph Memory for Mathematical Research Agents
Oct 2, 2026Junyi Zhang, Jinxi Yu, Eric Hanchen Jiang +14Autonomous Research Agents AI Agents for Scientific Discovery
University of California, Los Angeles
The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models
Oct 1, 2026Shuo Xing, Zilin Dai, Chengyuan Qian +7Mathematical Reasoning Benchmarks Self-Distillation
Texas A&M University · Harvard University · Vanderbilt University +3
Function-Structured Reinforcement Learning with Executable Verifiers for Mathematical Reasoning
Oct 1, 2026Zihan Liu, Xurong XieLLM Reasoning with Graphs RL for Language Model Reasoning
Department of Computer Science, University College London, UK · Institute of Software, Chinese Academy of Sciences, China
ReSolve: Reusing Candidate Reasoning through Selective Generative Moderation
Oct 1, 2026Bangji Yang, Jiajun Fan, Hongbo Ma +6Efficient Language Model Reasoning Inference-Time Compute Allocation
University of Illinois at Urbana-Champaign · Rutgers University · University of Illinois Chicago +2
Improving Math Reasoning through Value-guided Informative Search
Oct 1, 2026Shaohuai Liu, Yuning Wu, Haoran Liu +3RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards
Amazon · Department of Electrical and Computer Engineering, Texas A&M University
ANI: Adaptive Numerical Injection for Unifying Semantic and Arithmetic Representations in Numerical Reasoning
Sep 30, 2026Jinsung Jeon, Seung-won HwangNumerical Reasoning in Language Models LLM Mathematical Reasoning
KAIST InnoCORE LLM · Seoul National University · Korea University
Budget Boundary Effects in Test-Time Mathematical Reasoning
Sep 30, 2026Guilin Zhang, Ziqi Tan, Wulan Guo +5Mathematical Reasoning Benchmarks Test-Time Optimization
Yantong AI
Mathematical Transfer in LLMs Follows Reasoning Approach More Than Topic
Sep 29, 2026Sajad Goudarzi, Samaneh Zamanifard, Seyed Amin Seyed Haeri +2Transfer Learning LLM Mathematical Reasoning
Clemson University · Coastal Carolina University
Beyond Compression: Diagnosing How Post-Training Changes Mathematical Reasoning
Sep 29, 2026Hongyang Li, Yiming Zhu, Xiao Li +3Language Model Distillation RL Post-Training
University of Luxembourg · Seafill Open-Source Community · Université Paris-Saclay
Fine Until Fine-Tuned: Repeated Solutions Make Reasoning Fragile
Sep 27, 2026Ely SheikhContinual Learning for LLMs Data Repetition in Language Model Training
Aix-Marseille University
The Decomposition Tax: LLM Pipelines Lose Up to 40 Accuracy Points at Their Own Interfaces
Sep 26, 2026Tianqi Bu, YuXuan Peng, Junteng Tu +1LLM Grounding LLM Mathematical Reasoning
Rutgers University · Nanjing Tech University · Nanjing University of Posts and Telecommunications +1
Does CoT-Pass@k Really Check the CoT? A Multilingual Mathematical Audit
Sep 26, 2026Tarık Tuna Taşaltı, Burcu Hüdaverdi, David SemedoLLM-as-a-Judge LLM Mathematical Reasoning
Dokuz Eylül University, ˙Izmir, Türkiye · NOVA School of Science and Technology, Universidade NOVA de Lisboa, Caparica, Portugal
From Outcomes to Strategies: Learning Strategy Utility for Mathematical Reasoning
Sep 26, 2026Ruikang Zhang, Xiao An, Xuli Shen +5LLM Mathematical Reasoning RL for Language Model Reasoning
Peking University · Wuhan University · Shanghai Artificial Intelligence Laboratory +2
Solving Every Step Is Not Enough: Milestone Oracles Reveal a Composition Gap in LLM Math Reasoning
Sep 26, 2026Zhuohan Wang, Haoran Ma, Tianyu Wu +3LLM Mathematical Reasoning LLM Evaluation
Harvard University · Rutgers University · The Hong Kong University of Science and Technology
Order-Invariant Answers, Order-Sensitive Representations in Mathematical Reasoning
Sep 23, 2026Zhixu Silvia TaoMathematical Reasoning Representation Geometry in Language Models
Operations Research and Financial Engineering Princeton University Princeton, NJ 08540
Giving Credit Where It's Due: Redundancy-Aware Learning for Efficient Reasoning
Sep 22, 2026Yuqing Zhou, Hong Wang, Manqing Mao +8RL for Language Model Reasoning Step-Level Credit Assignment in RL
George Mason University · Amazon, Inc
Math Reasoning in LLMs is Organized by Approach, Not Topic
Sep 22, 2026Sajad Goudarzi, Samaneh Zamanifard, Moloud Nasiri +1Mathematical Reasoning Benchmarks LLM Interpretability
Clemson University
Construting Reverse Thinking: Developing Large Language Models' Reverse Thingking Ability
Sep 21, 2026Xin Liu, Yunhai Li, Chunfu Jia +2Efficient Language Model Reasoning LLM Mathematical Reasoning
China University of Petroleum (East China), Qingdao, China · College of Cryptology and Cyber Science, Nankai University, Tianjin, China · Goertek Inc., Qingdao, China

Oct 29, 2026J/K move · Enter open · S save

H $^2$ R: Hierarchical Hint-Based Reward for Mathematical Reasoning via Reinforcement Learning

He Tu, Siye Li, Hongyi Wen

New York University Shanghai

LLM Mathematical Reasoning Reward Shaping Reinforcement Learning with Verifiable Rewards Language Model Reasoning Evaluation

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Reinforcement Learning with Verifiable Rewards has shown great promise in enhancing mathematical reasoning in large language models. However, existing approaches provide limited intermediate supervision for complex, multi-step reasoning tasks. To bridge this gap, we propose Hierarchical Hint-based Reward, a framework that leverages the intrinsic sub-question structure of mathematical problems as structured intermediate conditioning signals during RLVR training. Unlike chain-of-thought prompting, these hierarchical hints serve as logically grounded intermediate milestones that effectively reduce the reasoning horizon toward the final answer. To validate this framework, we introduce HiMath, a benchmark of hierarchically structured mathematical problems. Across diverse LLMs, hierarchical hints consistently improve reasoning performance even without task-specific training. When integrated into RL training via H

^2

R, they boost Qwen2.5-Math-7B accuracy on HiMath from 30.4% to 39.1% using hierarchical hints, and up to 45.6% with Oracle Hierarchical Hints. This pronounced improvement demonstrates that incorporating reliable intermediate checkpoints into reward design is essential for sustaining complex mathematical reasoning.