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Use of AI in mathematical research - mklabgr - 09-11-2026
Use of AI in Mathematical Research: A Guide for Young Mathematicians — Pavel Etingof (MIT, May 2026)
Pavel Etingof argues that mathematicians should neither reject AI nor delegate mathematics to it. His central principle is simple: use AI to know and understand more mathematics, while personally remaining fully abreast of every mathematical step it produces. Any AI-generated proof, computation, or argument that enters one's work must be independently checked, understood in detail, and rewritten in the mathematician’s own way. The reason is both practical and educational: LLMs can produce convincing but subtly false arguments, and the researcher—not the AI—is responsible for errors. More fundamentally, struggling with problems is how mathematicians acquire intuition and research ability; outsourcing that struggle defeats much of the purpose of doing mathematics.
Etingof nevertheless sees AI as an increasingly powerful research instrument. It can help with literature searches, explanations, brainstorming research questions, generating examples and computational data, searching for counterexamples, writing code, LaTeX, and proofreading. For proving new results, however, he urges much greater skepticism: AI is considerably safer when explaining established mathematics than when claiming an original proof. One useful procedure is to have another model attack an AI-generated proof, iterate between critics, and then perform the decisive human verification yourself—but agreement between several models is still not evidence of correctness because models may share the same biases and failure modes. He also highlights formal verification with Lean, where LLMs can increasingly help translate mathematical statements into machine-checkable proofs, provided the human verifies that the formal statement actually represents the intended theorem.
The broader message is that AI should be treated as a powerful but unreliable digital collaborator, not an autonomous mathematician. Etingof recommends using it to increase the amount and depth of mathematics one can explore rather than to reduce one's own mathematical effort. Researchers should verify references, protect confidential material, avoid copying AI-generated prose, acknowledge substantial AI contributions, and remain capable of reproducing and explaining everything without access to the original AI conversation. He also stresses that mathematics is fundamentally communal: even a correct machine-generated proof does not become genuine mathematical understanding until humans interpret it, explain its ideas, connect it to existing knowledge, and make it accessible to the mathematical community.
Key takeaways
- AI should amplify mathematical thinking, not replace it.
- Treat every novel AI-generated proof as unverified until independently checked.
- AI may be especially useful for examples, counterexamples, computation, coding, literature search and Lean formalization.
- Etingof's final test is particularly strong: if the AI conversation disappeared, could you still understand, reproduce and take full responsibility for everything in your work?
ARTICLE [PDF]