First Proof is a public experiment that tests ArtificiaI Intelligence systems on real research mathematics. Working mathematicians write the problems, drawing each one from their own research. Several AI systems attempt them, and produce their best efforts at a solution. Experts in each problem's field then referee the solutions blind, the way they would review a journal submission, and the referee reports are published.

On October 8–9, 2026, the Institute for Computer-Aided Reasoning in Mathematics (ICARM) hosted the review of the third batch. About thirty reviewers worked in small groups to assess the AI-produced solutions. They covered ten problems from geometry, topology, statistics and dynamics. In the same two days, a second group of mathematicians met at ICARM to write and test the problems for the next batch.

Figure 1: Summary of how the five AI systems performed on the ten research problems (P1-P10).

The leading systems improved clearly on the previous round, and every problem was solved by at least one of them. Reviewers still found weaknesses in how the systems cited the literature and explained their arguments. Running the strongest systems also remains expensive.

On October 14, ICARM co-hosted a public webinar to present the results. ICARM Director Jeremy Avigad opened the session, and First Proof editor Mohammed Abouzaid (Stanford) gave an overview of the findings. One of the third batch's problem writers presented their problem, and all four editors took live questions: Abouzaid, Nikhil Srivastava (UC Berkeley), Rachel Ward (UT Austin) and Lauren Williams (Harvard). The webinar recording is available online, together with the press release and the full report, which includes the problem statements and referee reports. Discussion continues in the relevant channel on ICARM's public Zulip.