How AI is Changing the Nature of Mathematical Research

Modern AI coding tools have revolutionized software engineering, with developers now using AI assistants to write a substantial fraction of their code across a range of applications. As scientists studying the theory of machine learning, we’re already seeing a similar transformation in basic scientific methodology, especially for research of a mathematical nature.

More precisely, AI tools are now able to develop and write rigorous mathematical proofs only from prompts providing high-level proof sketches. These proofs are written in longstanding “languages” for detailing mathematical arguments, in the same way that code is written in formal programming languages like Python. AI seems to have become proficient in both kinds of languages and their underlying logics.

We came to this realization during a three-week period last summer, when we used agentic AI tools to write a mathematical paper that normally would have taken months.

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