Mathematical Reasoning

Follow this topic Ask about this topic

Mathematical reasoning asks how AI systems can solve multi-step problems, apply mathematical concepts, construct proofs, and help discover new results. Common approaches include supervised learning and reinforcement learning with verifiable rewards, alongside self-distillation, search, and structured methods that use code, symbolic solvers, or formal proof assistants such as Lean. Work spans arithmetic and competition problems, geometry, statistics, multimodal tasks, and research-level proofs, with benchmarks increasingly testing robustness, multilingual ability, and intermediate reasoning rather than answers alone. Models have improved on many standard tasks, but remain brittle under equivalent problem changes and difficult proof or construction demands; reliable verification, useful exploration, and meaningful measures of reasoning quality remain open challenges.

Latest papers

155 papers19 papers in the last four weeks, up 19% on the four weeks before. 0.1% of all new papers.

Beyond Selected Breakthroughs: Evaluating Language Models on Randomly Sampled Mathematical Conjectures
Oct 29, 2026Helen Jenne, Davis Brown, Jesse He +1LLM Mathematical Reasoning AI-Assisted Mathematical Discovery
Pacific Northwest National Laboratory · University of Pennsylvania · University of California San Diego +1
MASS: Multi-mask Selective Self-Distillation for Leakage-Resilient Reasoning
Oct 28, 2026Xiuqi Liu, Oveys Delafrooz Noroozi, Upamanyu MadhowLanguage Model Distillation Selective Knowledge Distillation
Chongqing Bashu Secondary School · University of California, Santa Barbara
Dependency Graphs of Mathematical Arguments: Representation, Structural Measurement, and Proof Review
Oct 27, 2026Eunji ParkMathematical Reasoning
Graduate School of Data Science, Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul 08826, Korea
Improving Reasoning with Rollout Agreement for Group-Based Policy Optimization
Oct 26, 2026Sohyun Son, Yerim Hong, Jaeyun Park +1Reinforcement Learning RL for Language Model Reasoning
Kyung Hee University, Yongin, Republic of Korea
SRA: Selective Residual Adaptation for LLM Reasoning Enhancement
Oct 25, 2026Zhenxing Dou, Kun He, Mingyang Yi +1Language Model Distillation Selective Knowledge Distillation
Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China · School of Information, Renmin University of China, Beijing, China
Steering the Teacher: Improving On-Policy Self-Distillation for Thinking Models
Oct 25, 2026Tiejin Chen, Xiaoou Liu, Hanyang Chen +1On-Policy Self-Distillation Citation Hallucination
Arizona State University
Edit, Don't Imitate: Minimal-Edit On-Policy Distillation for Multimodal Reasoning
Oct 21, 2026Wen Ye, Ailin Deng, Zirui Wang +8Reasoning for VLMs Vision-Language Models
Meta Superintelligence Labs · University of Southern California · University of California, Berkeley +2
VASPO: Self-Distillation with Privileged Value Estimation
Oct 14, 2026Fei Wu, Zhenrong Zhang, Jianshu Zhang +1RL for Language Model Reasoning On-Policy Self-Distillation
University of Science and Technology of China · IFLYTEK Research
Euler: Towards Human-Centered Multi-Agent Mathematical Discovery
Oct 14, 2026Qiuyu Chen, Qi Wang, Liang Xu +3AI-Assisted Mathematical Discovery Autonomous Research Agents
Shanghai Jiao Tong University · Ningbo Key Laboratory of Spatial Intelligence and Digital Derivative, Ningbo Institute of Digital Twin, Eastern Institute of Technology, Zhejiang, China · Institute of Automation, Chinese Academy of Sciences +1
GAGR-Lab: Evaluating Joint Spatial-Geometric and Analytic Function Reasoning
Oct 7, 2026Jingyao Zhang, Yun Li, Lu HanSpatial Reasoning Benchmarks Mathematical Reasoning
A Drosophila Whole-Connectome Network Can Learn Human-Designed Cognitive Tasks
Oct 7, 2026Joonghui Cho, Minchan Kang, Daeshik KimMathematical Reasoning
Korea Advanced Institute of Science and Technology (KAIST)
Teaching a Minimalist Machine to Discover Recursive Programs for Arithmetic
Oct 5, 2026Dominik Magiera, Christiane Wiebel-Herboth, Frank JäkelCognitive Modeling Program Synthesis
Centre for Cognitive Science & Institute of Psychology, Technische Universität Darmstadt, Germany · Honda Research Institute Europe GmbH, Offenbach am Main, Germany
Transfer-Stratified On-Policy Distillation for RL-Improved Reasoning Teachers
Oct 5, 2026Xiaoyu Chen, Bo Shao, Tiangang Zhu +5RL for Language Model Reasoning Selective Knowledge Distillation
Institute of Software, Chinese Academy of Sciences · Microsoft · Work done during an internship at Microsoft +1
E $^2$ -OPSD: Taming Entropy Overshoot in On-Policy Self-Distillation
Oct 4, 2026Yifei Liu, Minghao Fang, Xinyu Gu +6On-Policy Self-Distillation Mathematical Reasoning
The Chinese University of Hong Kong · Zhejiang University · Shanghai Artificial Intelligence Laboratory +5
Questioning the Questions: Sustaining Self-Evolution in Reasoning Models
Oct 3, 2026Jinyuan Li, Chengsong Huang, Langlin Huang +4Language Model Self-Improvement Self-Training for Language Models
Washington University in St. Louis · University of Michigan, Ann Arbor
Dense Neuro-Symbolic Reasoning in a Unified Geometry State
Oct 3, 2026Ruoran Xu, Wending Gao, Haoyu Cheng +2Mathematical Reasoning Neuro-Symbolic Reasoning
Xi’an Jiaotong-Liverpool University
Learning from Evolving Errors: Adaptive Iterative Repair for On-Policy Distillation
Oct 2, 2026Rui Li, Liyang He, Zheng Zhang +3On-Policy Self-Distillation On-Policy Distillation
University of Science and Technology of China · Nanyang Technological University
SCB: SpeechConversationBench for Evaluating Multi-Turn Reasoning in Speech-to-Speech Models
Sep 30, 2026Kanpat Vesessook, Saksorn RuangtanusakNumerical Reasoning in Language Models Mathematical Reasoning
SCBX R&D · SCB DataX, SCBX Group
Better Supervision Is Nearby: Neighborhood On-Policy Self-Distillation
Sep 30, 2026Xincheng Wei, Yifan Ding, Yoshua Li +6On-Policy Self-Distillation Mathematical Reasoning
The Chinese University of Hong Kong, Shenzhen · Meituan, LongCat Team · University of Toronto +1
T-Router: Learning Thalamic Routing for Reasoning with Parameter-Efficient Reinforcement Learning
Sep 30, 2026Liuxian Ma, Jiale Dai, Jiaqi Li +1Reinforcement Learning RL for Language Model Reasoning
College of Artificial Intelligence, Tsinghua University · State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University · Beijing Institute for General Artificial Intelligence
Evidence First, Arithmetic Second: A System Report and Failure Analysis for DocSem
Sep 30, 2026Divya Godara, Sachin GuptaDocument QA Mathematical Reasoning
Independent Researcher San Jose, USA
Overcoming Scaling Limits in On-Policy Self-Distillation for LLM Reasoning
Sep 29, 2026Md. Ismail Hossain, Humaira Kousar, Isidora Chara TourniOn-Policy Self-Distillation Mathematical Reasoning
North South University · KAIST · Andria Labs
Mathematics for and by human cognition: A resource-rational search for bottlenecks in problem-solving
Sep 28, 2026Sneha AenuguMathematical Reasoning Bounded Rationality
Salk Institute of Biological Studies La Jolla, CA
Towards Eliminating Catastrophic Forgetting in the Curriculum Learning of Math Reasoning Tasks
Sep 27, 2026Zengyan Yang, Yangyang Wu, Kai Huang +3Elastic Weight Consolidation Mathematical Reasoning
Zhejiang University · Ant Group
Quizzing the Translation: A Prover-Grounded Evaluation Metric for NL $\rightarrow$ FOL
Sep 27, 2026Pu Suo, Ali EmamiLanguage Model Error Detection Mathematical Reasoning
Emory University
Reasoning on the Simplex: Geometric Fixed-Point Models
Sep 27, 2026Talgat Daulbaev, Ilya Glazkov, Maxim Rakhuba +1Mathematical Reasoning Recursive Language Models
Applied AI Institute · LigandPro · HSE University +1
Structure-Mapping-Guided Self-Explanation for Learning Mathematical Procedures
Sep 27, 2026Shinhaeng Lee, Christopher J. MacLellan, Daniel WeitekampComputational Cognitive Modeling Mathematical Reasoning
Georgia Institute of Technology, Atlanta, GA 30332 USA
Learning from a Thoughtful Teacher: Adaptive On-Policy Self-Distillation for Mathematical Reasoning
Sep 26, 2026Jiacheng Du, Weiwei Xie, Tianyi Du +3On-Policy Self-Distillation CoT Distillation
National University of Singapore · Shanghai Jiao Tong University · Shanghai Artificial Intelligence Laboratory
Recursive Self-Improvement via On-Policy Distillation for Reasoning
Sep 25, 2026Shangjian Yin, Zehao Zhao, Kavosh Asadi +7Language Model Self-Improvement On-Policy Self-Distillation
Meta AI · University of California, Riverside · Work done at Meta
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

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

Beyond Selected Breakthroughs: Evaluating Language Models on Randomly Sampled Mathematical Conjectures

Helen Jenne, Davis Brown, Jesse He, Henry Kvinge

Pacific Northwest National Laboratory · University of Pennsylvania · University of California San Diego+1

LLM Mathematical Reasoning AI-Assisted Mathematical Discovery Language Model Reasoning Evaluation Mathematical Reasoning Faithfulness of Language Model Reasoning

Open paper AskPDF arXiv

The last year has seen a shift in AI-assisted mathematics, with frontier language models producing proofs of and counterexamples to long-standing open conjectures. However, studying only the current set of major breakthroughs provides an incomplete picture of LLM capabilities and the computational resources needed to achieve reported results. To address this, we introduce a new dataset, OpenConjecture, which collects conjectures from mathematics papers published on the arXiv since February 2026. We use these conjectures as a source of open mathematical problems, and apply frontier GPT models to a random sample of 200 of these conjectures over three passes using a reproducible protocol without problem-specific mathematical guidance. Rather than attempt expert verification of these candidate solutions, we analyze the types of problems for which LLMs produce solutions and the characteristics of these solutions. The models we test produce candidate solutions for roughly 60% of the conjectures, with counterexamples about 1.3 times more common than proofs. We estimate solution novelty, assess how solutions cite and relate to existing literature, and analyze whether the proposed resolution relies on either an error in or underspecification of the conjecture. We find that models sometimes propose resolutions that are outside the authors' intent (e.g., proposing the trivial group as a counterexample) and that a number of proofs follow closely from existing results, but that some resolutions exhibit at least moderate novelty. Our findings underscore the need for evaluations that go beyond correctness to assess fidelity to the intended statement, attribution, and the nature of the mathematical contribution.