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Mathematical Discovery in the Wild: AI-Guided Proofs in Banach Space Theory

arXiv 2607.17388 ↗First posted 19 Jul 2026math.FA cs.AIcited by 0

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Abstract (arXiv)

We investigate the capacity of current language models to contribute to mathematical research. In Banach space theory, AI systems generated key ideas and proofs for five new results, which were then verified and refined by humans. We also developed an automated system that searches the literature for open problems and attempts solutions at scale. Our results show both the potential of language models for mathematical discovery and the continuing importance of expert verification.

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References · 18

  1. 2024The AI Scientist: Towards Fully Automated Open-Ended Scientific Discoverycited by 1,071
  2. 2025AlphaEvolve: A coding agent for scientific and algorithmic discoverycited by 867
  3. 2025The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Searchcited by 422
  4. 2024FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AIcited by 243
  5. 2025Kosmos: An AI Scientist for Autonomous Discoverycited by 92
  6. 2025Mathematical exploration and discovery at scalecited by 77
  7. 2025Aristotle: IMO-level Automated Theorem Provingcited by 58
  8. 2026Towards Autonomous Mathematics Researchcited by 40
  9. 2026First Proofcited by 32
  10. 2026Automated Conjecture Resolution with Formal Verificationcited by 28
  11. 2026Toward Generalist Autonomous Research via Hypothesis-Tree Refinementcited by 22
  12. 2026AI co-mathematician: Accelerating mathematicians with agentic AIcited by 17
6 more
  1. 2025IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generationcited by 13
  2. 2025Generative Modeling for Mathematical Discoverycited by 10
  3. 2026LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematicscited by 10
  4. 2026Aletheia tackles FirstProof autonomouslycited by 9
  5. 2026First Proof Second Batchcited by 6
  6. 2026Iteris: Agentic Research Loops for Computational Mathematicscited by 3

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