AI-Assisted Mathematical Discovery

Follow this topic Ask about this topic

Latest papers

22 papers6 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Recursive Reasoning Exploration: Mathematical Research through Evolving Reasoning Graphs : case study: An Exact Certificate-Degree Theorem for Two-Term Tensor Decompositions : Phase III of the Math Instruments Program
Nov 1, 2026Ying XieMathematical Reasoning AI-Assisted Mathematical Discovery
Kennesaw State University
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
PACE: Research Proving Agent for Adaptive Conjecture Exploration
Oct 24, 2026Shu Miao, Feiming Wang, Wentao Long +3AI-Assisted Mathematical Discovery Autonomous Research Agents
Peking University · Nankai University · Fudan University
Breaking the high-degree barrier in Lehmer's problem with a human-AI discovery loop
Oct 21, 2026Yuri Chervonyi, Sergei Gukov, Thang LuongAI-Assisted Mathematical Discovery
Google DeepMind · California Institute of Technology
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
What the Machine Invented: Mining New Mathematical Instruments from OpenAI's October 2026 Release of AI-Generated Mathematics
Oct 12, 2026Ying XieAI-Assisted Mathematical Discovery AI-Assisted Scientific Research
Kennesaw State University
GenLimitLib: A Formal Library for Language Generation in the Limit and AI-Assisted Mathematical Research
Sep 29, 2026Shuangping Li, Peng ZhangAI-Assisted Mathematical Discovery Text Generation
Yale University · Rutgers University
Learning to Discover Interesting Mathematics
Sep 23, 2026Niket Patel, Ahmad Rammal, Amaury Hayat +2Automated Theorem Proving Lean Theorem Proving
New York University · CERMICS, ENPC, Institut Polytechnique de Paris
AI-Assisted Discovery and Construction of a Counterexample to the Convergence of Three-Block ADMM with the Identity Matrix as its Third Constraint Block
Aug 14, 2026Kenan Xu, Xiangfeng WangAI-Assisted Mathematical Discovery Alternating Direction Method of Multipliers
School of Mathematical Sciences, East China Normal University, Shanghai 200241, P.R. China. · Key Laboratory of Mathematics and Engineering Applications (MoE) and School of Mathematical Sciences, East China Normal University, Shanghai 200241, P.R. China.
Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration
Aug 11, 2026Alan Li, Rahul Saha, Anton Xue +4Deep Research Agents AI-Assisted Mathematical Discovery
Neurosymbolic Discovery of Algebraic Graph Constructions
Aug 8, 2026David Seka, Stefan SzeiderGraph Construction Neuro-Symbolic Reasoning
Algorithms and Complexity Group TU Wien, Vienna, Austria
Mathematical Discovery in the Wild: AI-Guided Proofs in Banach Space Theory
Jul 19, 2026Antonio Acuaviva, Pablo AcuavivaAutomated Theorem Proving AI-Assisted Mathematical Discovery
ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent System
Jul 15, 2026Yutong He, Daibo Li, Guohong Li +15Multi-Agent LLM Systems AI Agents for Scientific Discovery
Peking University · University of Electronic Science and Technology of China · Beijing Normal University +2
Language models guide symbolic equation discovery by controlling search
Jul 5, 2026Zikai Xie, Wenmei Li, Man Luo +2Large Language Model-Guided Scientific Discovery Symbolic Regression
State Key Laboratory of Precision and Intelligent Chemistry, Hefei National Research Center for Physical Sciences at the Microscale, School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, China. · Center for Scientific Intelligence Innovation, Hefei, China · School of Chemistry, School of Computer Science, University of Birmingham, Birmingham, UK
Nothing from Something: Can a Language Model Discover 0?
Jun 15, 2026Phoebe Zeng, Thomas L. Griffiths, Brenden M. LakeNumerical Reasoning in Language Models Language Model Pretraining
Department of Computer Science, Princeton University
Iteris: Agentic Research Loops for Computational Mathematics
Jun 1, 2026Leheng Chen, Zihao Liu, Wanyi He +1Mathematical Reasoning Large Language Model-Guided Scientific Discovery
School of Mathematical Sciences, Peking University · 5Zhongguancun Academy · 2Beijing International Center for Mathematical Research and the New Cornerstone Science Laboratory, Peking University +2
AI co-mathematician: Accelerating mathematicians with agentic AI
May 7, 2026Daniel Zheng, Ingrid von Glehn, Yori Zwols +15AI Agents for Scientific Discovery AI-Assisted Mathematical Discovery
Google DeepMind · Google
Grokability in five inequalities
May 6, 2026Paata Ivanisvili, Xinyuan XieAI-Assisted Mathematical Discovery
University of California, Irvine
Yanasse: Finding New Proofs from Deep Vision's Analogies, Part 1
Apr 19, 2026Alexandre LinharesAutomated Theorem Proving Analogical Reasoning
Getulio Vargas Foundation · ARGO LABS
$k$ -server-bench: Automating Potential Discovery for the $k$ -Server Conjecture
Apr 8, 2026Kirill Brilliantov, Etienne Bamas, Emmanuel AbbéAI-Assisted Mathematical Discovery Autonomous Scientific Discovery
MDS Lab, EPFL
Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification
Mar 16, 2026Erik Y. Wang, Sumeet R. Motwani, James V. Roggeveen +9Mathematical Reasoning Benchmarks LLM Mathematical Reasoning
Stanford University · Benchmark · University of Oxford +3
AI Mathematician: Towards Fully Automated Frontier Mathematical Research
May 28, 2025Yuanhang Liu, Yanxing Huang, Yanqiao Wang +2AI-Assisted Mathematical Discovery AI-Assisted Scientific Research
Qiuzhen College, Tsinghua University · Department of Mathematical Sciences, Tsinghua University · Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China +1

Nov 1, 2026J/K move · Enter open · S save

Recursive Reasoning Exploration: Mathematical Research through Evolving Reasoning Graphs : case study: An Exact Certificate-Degree Theorem for Two-Term Tensor Decompositions : Phase III of the Math Instruments Program

Ying Xie

Kennesaw State University

Mathematical Reasoning AI-Assisted Mathematical Discovery Tensor Decomposition

Open paper AskPDF arXiv

Large collections of manuscripts and research notes offer ways to reuse arguments, while making it harder to retain hypotheses, check claims, and understand how results were obtained. We propose Recursive Reasoning Exploration (RRE), a framework for cumulative mathematical research through evolving reasoning graphs. RRE links claims and jointly required premises to research targets, attempted arguments, counterexamples, checks, and revisions. Each investigation can generate further targets, and its supported outcomes become available to subsequent investigations. This is Phase III of the Math Instruments program: identifying mathematical instruments, reconstructing reusable reasoning, and organizing recursive research from that reasoning. The framework supports human-directed, collaborative, and goal-directed autonomous exploration, with open-ended exploration as a further mode. Its records also provide material for learning how mathematical investigations develop. A complexity research case study establishes an exact theorem: for every complex tensor of order n >= 2 and rank greater than two, the minimum Nullstellensatz certificate degree for its original two-term decomposition equations is 3n. This includes an infinite family whose every flattening has rank at most two. The exploration develops an explicit boundary certificate, a balanced transfer lemma, and an exhaustive argument using classical rank-two geometry. A parallel branch gives bounds 3m + 3 <= delta_m(I_m, N) <= 3m + 6 for every nonzero nilpotent m by m matrix. Six graph revisions record the progression from inherited results to these theorems, with exact arithmetic checks and a replayable exploration history. We present the RRE representation and protocol, the mathematical proofs, visualizations of graph evolution, and a research agenda for shared human-AI exploration, cumulative reuse, and education.