Can AI do research math?

The video provides a valuable and insightful discussion on the capabilities and limitations of AI in research mathematics, based on the direct experience of the First Proof project. The speakers are highly credible, being leading researchers in theoretical computer science and mathematics, and they offer a balanced perspective, acknowledging both the impressive achievements and the significant challenges. The argumentation is solid, grounded in concrete examples from the first round of problems. They highlight the critical issue of verification, which is often overlooked in AI benchmarks, and the difficulty of assessing solutions that are not easily gradable. The discussion also touches on the different ‘voices’ of LLMs, which is a nuanced observation about the behavior of these systems. The sources are not explicitly cited, but the context of the First Proof project and the speakers’ expertise lend credibility. The title accurately reflects the content. The main limitation is that the discussion is anecdotal and based on a small sample of problems, but this is acknowledged by the speakers. Overall, the video offers a thoughtful and expert perspective on a timely topic, making it a valuable resource for those interested in the intersection of AI and mathematics.

The title is a concise and accurate summary of the discussion, which focuses on the capabilities of AI in research mathematics.

8/10

Discussion by leading researchers in theoretical computer science and mathematics, based on direct experience from the First Proof project. The claims are anecdotal but grounded in a concrete experiment, and the speakers are credible experts.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 00:00Introduction by Venkat Guruswami, setting the context of the First Proof project and its second round announcement.
• 02:00Nikhil Srivastava explains the motivation for First Proof: to avoid selection bias and provide a clear picture of AI capabilities across different areas of mathematics.
• 05:00Dan Spielman discusses his interest in using LLMs for his own research and the importance of testing publicly available models rather than proprietary ones.
• 08:00The speakers describe the criteria for selecting problems: they arose naturally from their research, with a range of difficulties, and were not designed to be easily gradable.
• 10:00Nikhil reflects on the surprising interest from the math community and AI companies, and the unexpected number of solutions produced in the first round.
• 12:00Dan discusses the different 'voices' of LLMs, including overconfident and deceptive ones, and the improvement of some models in admitting uncertainty.
• 15:00The challenge of verification is highlighted, with Nikhil comparing it to a reverse P vs NP problem: generation is easy, verification is hard.
• 18:00The involvement of the formalization community is mentioned, with LEAN proofs produced for three solutions, which is seen as amazing.
• 20:00Dan shares an example where an AI critique of proofs found errors in his own work that human reviewers missed, showing the potential of AI for verification.
• 25:00The speakers discuss the distrust that arises from using LLMs, and the potential for formal proofs to increase trust.

• First Proof — Mentioned as the project that benchmarks AI on research mathematics.

• First Proof — The project's website, which provides details on the benchmark and results.