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

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

Preventing Curriculum Collapse in Self-Evolving Reasoning Systems
Mar 3, 2026Vaibhav MishraMathematical Problem Generation Language Model Self-Improvement
When Shallow Wins: Silent Failures and the Depth-Accuracy Paradox in Latent Reasoning
Mar 3, 2026Subramanyam Sahoo, Aman Chadha, Vinija Jain +1LLM Mathematical Reasoning Reasoning Consistency in Language Models
Independent · AWS Generative AI Innovation Center, Amazon Web Services · Stanford University +2
NeuroProlog: Multi-Task Fine-Tuning for Neurosymbolic Mathematical Reasoning via the Cocktail Effect
Mar 3, 2026Pratibha Zunjare, Michael HsiaoLLM Mathematical Reasoning Neuro-Symbolic Reasoning
Electrical and Computer Engineering, Virginia Tech, Blacksburg, USA
Learn Hard Problems During RL with Reference Guided Fine-tuning
Mar 1, 2026Yangzhen Wu, Shanda Li, Zixin Wen +5LLM Mathematical Reasoning RL for Language Model Reasoning
UC Berkeley · Carnegie Mellon University · ByteDance Seed
Evaluating AI Grading on Real-World Handwritten College Mathematics: A Large-Scale Study Toward a Benchmark
Mar 1, 2026Zhiqi Yu, Xingping Liu, Haobin Mao +4Automated Grading Generative AI in Education
UC Irvine Irvine, USA · Independent Shanghai, China · UC Berkeley Berkeley, USA
LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematics
Feb 27, 2026Antoine Peyronnet, Fabian Gloeckle, Amaury HayatMathematical Reasoning Benchmarks Automated Theorem Proving
1Ecole Normale Superieure de Rennes · 2Ecole des Ponts Paris · 3Korean Institute for Advanced Study
Strategy Executability in Mathematical Reasoning: Leveraging Human-Model Differences for Effective Guidance
Feb 26, 2026Weida Liang, Yiyou Sun, Shuyuan Nan +3LLM Mathematical Reasoning Inference-Time Guidance
National University of Singapore · University of California, Berkeley
GeoChallenge: A Multi-Answer Multiple-Choice Benchmark for Geometric Reasoning with Diagrams
Feb 25, 2026Yushun Zhang, Weiping Fu, Zesheng Yang +6Mathematical Reasoning Benchmarks LLM Mathematical Reasoning
School of Computer Science and Technology, Xi’an Jiaotong University, Xi’an, China · Shaanxi Province Key Laboratory of Big Data Knowledge Engineering, Xi’an, China
Aletheia tackles FirstProof autonomously
Feb 24, 2026Tony Feng, Junehyuk Jung, Sang-hyun Kim +14LLM Mathematical Reasoning Autonomous Research Agents
Google DeepMind · UC Berkeley · Brown University +7
Linear Reasoning vs. Proof by Cases: Obstacles for Large Language Models in FOL Problem Solving
Feb 24, 2026Yuliang Ji, Fuchen Shen, Jian Wu +2Logical Reasoning Mathematical Reasoning
Nanjing University of Science and Technology · Westlake University · Zhejiang University
Pipeline for Verifying LLM-Generated Mathematical Solutions
Feb 24, 2026Varvara Sazonova, Dmitri Shmelkin, Stanislav Kikot +1LLM Answer Verification LLM Evaluation
Moscow State University · Huawei Technologies Co., Ltd
Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)
Feb 21, 2026Brecht Verbeken, Brando Vagenende, Marie-Anne Guerry +2Large Language Model-Guided Theorem Proving LLM Mathematical Reasoning
Data Analytics Lab, Vrije Universiteit Brussel, Pleinlaan 5, 1050 Brussel, Belgium · imec-SMIT, Vrije Universiteit Brussel, Pleinlaan 9, 1050 Brussels, Belgium · School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Ontology-Guided Neuro-Symbolic Inference: Grounding Language Models with Mathematical Domain Knowledge
Feb 19, 2026Marcelo LabreRetrieval-Augmented Generation LLM Grounding
Advanced Institute for Artificial Intelligence (AI2)
Process Rewards for Outcome-Guided Reasoning Steps in LLM Reinforcement Learning
Feb 8, 2026Mohammad Rezaei, Jens Lehmann, Sahar VahdatiLLM Mathematical Reasoning Reinforcement Learning
Faculty of Computer Science, Technical University of Dresden, Dresden, Germany · Amazon Science · Technical University of Dresden, Dresden, Germany +1
MGSM-Pro: A Simple Strategy for Robust Multilingual Mathematical Reasoning Evaluation
Jan 29, 2026Tianyi Xu, Kosei Uemura, Alfred Malengo Kondoro +6Numerical Reasoning in Language Models Mathematical Reasoning Benchmarks
McGill University · Mila-Quebec AI Institute · University of Toronto +7
The Effect of Scripts and Formats on LLM Numeracy
Jan 21, 2026Varshini Reddy, Craig W. Schmidt, Seth Ebner +3Numerical Reasoning in Language Models Multilingual Language Model Evaluation
Kensho Technologies · Ben-Gurion University · MIT Cambridge, MA
MINIF2F-DAFNY: LLM-Guided Mathematical Theorem Proving via Auto-Active Verification
Dec 11, 2025Mantas Baksys, Stefan Zetzsche, Olivier Bouissou +1Automated Theorem Proving Formal Verification
University of Cambridge, Cambridge, UK · Amazon Web Services, London, UK · Amazon Web Services, Boston, USA
ScalePRM: Training Process Reward Models by Scaling Verification Compute Without Ground Truth
Dec 2, 2025Salman Rahman, Sruthi Gorantla, Arpit Gupta +3Process Reward Models Reinforcement Learning with Verifiable Rewards
2UCLA · Work done while as an intern at Amazon AGI. · 1Amazon AGI
Pessimistic Verification for Open Ended Math Questions
Nov 26, 2025Yanxing Huang, Zihan Tang, Zejin Lin +2LLM Answer Verification LLM Mathematical Reasoning
Qiuzhen College, Tsinghua University, Beijing, China · Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China · Dept. of Comp. Sci & Tech., Institute for AI, Tsinghua University, Beijing, China.
Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis
Nov 13, 2025Yongxian Wei, Yilin Zhao, Li Shen +7Synthetic Data Generation Synthetic Data Generation for Language Models
Tsinghua University · Tencent · Sun Yat-sen University +1
OpenSIR: Open-Ended Self-Improving Reasoner
Nov 1, 2025Wai-Chung Kwan, Joshua Ong Jun Leang, Pavlos Vougiouklis +3Self-Play RL RL for Language Model Reasoning
University of Edinburgh · Imperial College London · Huawei Technologies Research & Development (UK) Limited +1
TopoAlign: A Framework for Aligning Code to Math via Topological Decomposition
Oct 13, 2025Yupei Li, Philipp Borchert, Gerasimos LampourasAutomated Theorem Proving Autoformalization
1Imperial College London, UK · *Work conducted during an internship at Huawei Noah’s Ark Lab, London. · 2Huawei Noah’s Ark Lab, London, UK
Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graph
Oct 6, 2025Hanyu Wang, Ruohan Xie, Yutong Wang +3Lean Theorem Proving Autoformalization
Peking University · Institute for Artificial Intelligence, Peking University · IQuest Research +4
IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
Sep 30, 2025Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck +57Mathematical Reasoning Benchmarks LLM Evaluation
Learning How to Use Tools, Not Just When: Pattern-Aware Tool-Integrated Reasoning
Sep 27, 2025Ningning Xu, Yuxuan Jiang, Shubhashis Roy Dipta +1Tool-Integrated Reasoning LLM Tool Use
University of Georgia · University of Maryland, Baltimore County · 3The University of Hong Kong
Generative AI performance in core undergraduate mathematics: a curriculum-level case study
Sep 15, 2025Benjamin J. Walker, Nikoleta Kalaydzhieva, Beatriz Navarro Lameda +1Educational Assessment Generative AI in Education
Department of Mathematics, University College London, Gordon Street, WC1H 0AY, London, UK
An Investigation of Robustness of LLMs in Mathematical Reasoning: Benchmarking with Mathematically-Equivalent Transformation of Advanced Mathematical Problems
Aug 12, 2025Yuren Hao, Xiang Wan, ChengXiang ZhaiMathematical Reasoning LLM Mathematical Reasoning
Department of Computer Science University of Illinois Urbana–Champaign Urbana, IL, USA · Department of Computer Science Stanford University Stanford, CA, USA
Formally Solving Answer-Construction Problems in Lean
May 24, 2025Jialiang Sun, Yuzhi Tang, Ao Li +2Lean Theorem Proving LLM Mathematical Reasoning
University of Toronto, Toronto, Canada · Georgia Institute of Technology, Atlanta, USA
EquivPruner: Boosting Efficiency and Quality in LLM-Based Search via Action Pruning
May 22, 2025Jiawei Liu, Qisi Chen, Jianshu Zhang +2LLM Inference Efficiency Semantic Textual Similarity
School of Computer Science and Technology, University of Science and Technology of China · Department of Data Science, City University of Hong Kong · iFLYTEK Research
Reliable Proof Generation with LLMs via Analogical Retrieval and Symbolic Verification: A Case Study in Euclidean Geometry
May 20, 2025Oren Sultan, Eitan Stern, Dafna ShahafAutomated Theorem Proving Neuro-Symbolic Reasoning
The Hebrew University of Jerusalem

Mar 3, 2026J/K move · Enter open · S save

Preventing Curriculum Collapse in Self-Evolving Reasoning Systems

Vaibhav Mishra

Mathematical Problem Generation Language Model Self-Improvement Self-Evolving Agents LLM Mathematical Reasoning

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Self-evolving reasoning frameworks let LLMs improve their reasoning capabilities by iteratively generating and solving problems without external supervision, using verifiable rewards. Ideally, such systems are expected to explore a diverse problem space and propose new challenges of high learning value. While prior work has largely focused on solver-side optimisation and verification, recent evidence suggests that self-evolving systems can exhibit diversity collapse in posing new problems after just a few iterations, even when surface-level variation is preserved. We introduce Prism, a question-centric self-evolution method that directly tackles this collapse. Prism defines a persistent diversity signal over an embedding-induced semantic partition of mathematical problems and uses it to encourage balanced exploration of underrepresented regions across iterations. This coverage signal is combined with a Zone-of-Proximal-Development (ZPD) gate to preserve edge-of-solvability difficulty. Evaluated on seven widely used mathematical reasoning benchmarks against five self-evolving baselines, Prism achieves the highest accuracy on six out of seven tasks, achieving gains of +3.98 absolute points over R-Zero on AMC and +3.68 on Minerva Math. Prism also generates semantically diverse and challenging questions across iterations, resulting in the construction of the Prism-Math dataset comprising 100k mathematical questions. These results demonstrate that cross-iteration semantic coverage is a high-leverage and under-explored axis for building more capable self-evolving reasoners. We release the code, dataset, and models to facilitate further research.