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

Antonio Acuaviva, Pablo Acuaviva

arXiv:2607.17388v1 Primary: math.FA Secondary: cs.AI

Abstract

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.

Disclosure

“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 bot”
arXiv metadata: abstract

Classification: Substantial mathematical content or result generation
Multiplier: 10
Verified: 2026-08-23T18:58:14.371256Z

Structural counts

Pages 141 pdf

Theorems 13 source

Lemmas 36 source

Propositions 6 source

Corollaries 3 source

Definitions 12 source

Displayed equations 784 source

Bibliography entries 75 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file main.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.