mlsanityData to 7 Oct 2026

Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problems

arXiv 2601.22401 ↗First posted 29 Jan 2026cs.AI math.CO math.NTcited by 24

Not on the map. Why?

Abstract (arXiv)

We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's ErdHos Problems database. We employ a hybrid methodology: AI-driven natural language verification to narrow the search space, followed by human expert evaluation to gauge correctness and novelty. We address 13 problems that were marked 'Open' in the database: 5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature. Our findings suggest that the 'Open' status of the problems was through obscurity rather than difficulty. We also identify and discuss issues arising in applying AI to math conjectures at scale, highlighting the difficulty of literature identification and the risk of ''subconscious plagiarism'' by AI. We reflect on the takeaways from AI-assisted efforts on the ErdHos Problems.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 0 of its 46 references that are in the map. First posted on arXiv 29 Jan 2026.

Builds on

0 of 46 references.

No references here yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 24.

24 papers.

Sort:

By area:

  1. 2026Towards Autonomous Mathematics Researchcited by 31
  2. 2026Automated Conjecture Resolution with Formal Verificationcited by 21
  3. 2026LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworkscited by 11
  4. 2026LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematicscited by 7
  5. 2026Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verificationcited by 7
  6. 2026Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibriumcited by 7
  7. 2026Aletheia tackles FirstProof autonomouslycited by 6
  8. 2026GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithmscited by 6
  9. 2026Closing the Loop to Discover Psychological Theories with an Automated Cognitive Scientistcited by 6
  10. 2026EsoLang-Bench: Evaluating Genuine Reasoning in Large Language Models via Esoteric Programming Languagescited by 4
  11. 2026Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMscited by 4
  12. 2026Evolution Fine-Tuning: Learning to Discover Across 371 Optimization Taskscited by 4
12 more
  1. 2026How Open Must Language Models be to Enable Reliable Scientific Inference?cited by 2
  2. 2026Discovering mathematical concepts through a multi-agent systemcited by 1
  3. 2026An Enigma of Artificial Reason: Investigating the Production-Evaluation Gap in Large Reasoning Modelscited by 1
  4. 2026From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontiercited by 1
  5. 2026Artificial Organisationscited by 0
  6. 2026k-server-bench: Automating Potential Discovery for the k-Server Conjecturecited by 0
  7. 2026Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discoverycited by 0
  8. 2026Grokability in five inequalitiescited by 0
  9. 2026SCALAR: A Neurosymbolic Framework for Automated Conjecture and Reasoning in Quantum Circuit Analysiscited by 0
  10. 2026Using large language models to probe the limits of atom-centered structural descriptorscited by 0
  11. 2026How Good Are Frontier Models at Physics? Expert Re-Grading Reveals Broken Evaluations and Near-Saturation of Leading Benchmarkscited by 0
  12. 2026From Expert-Guided Proof Search to Automated Open-Problem Solvingcited by 0