Terence Tao Criticizes OpenAI's 719 AI Proofs for Lack of Transparency and Undermining Mathematical Community

IT Home previously reported that OpenAI initially published a total of 722 AI-generated mathematical manuscripts on GitHub on October 6, covering 372 result families and several open research problems. However, three manuscripts were withdrawn on October 7 due to a symbol error and its cascading effects, bringing the current public catalog to 719 manuscripts.

OpenAI stated that prior to publication, it consulted the "Advisory Group on Mathematics and Artificial Intelligence" (AGMAI), hosted by the Institute for Advanced Study at Princeton, and referenced its public recommendations. However, based on publicly available information, this release has not yet fully met the standards proposed by the group.

AGMAI had previously recommended that frontier AI labs stop testing high-difficulty mathematical problems on proprietary models inaccessible to outsiders, and required disclosure of model names, prompts, reasoning chains, time taken, and computational costs; however, OpenAI still used proprietary models in this instance, and only 10 manuscripts included model reasoning chains.

Regarding human understandability, the advisory group emphasized that AI-generated proofs should be easy for mathematicians to review and learn from; but reportedly, approximately 42% of the proofs released by OpenAI have not been formalized, nor do they provide machine-readable metadata linking natural language proofs with formal artifacts.

AGMAI also declared that its advisory role does not constitute an endorsement of OpenAI’s acquisition or publication of these results, and that the mathematics community must ultimately assess whether the relevant recommendations have been adequately implemented. This incident has once again sparked controversy regarding the transparency, formal verification, peer review, and academic autonomy of AI-generated mathematical achievements.

On October 7, Terence Tao posted on Mathstodon, stating that he is not opposed to AI doing mathematics and has even been an active user of AI-assisted research; but he strongly opposes making "using AI to quickly conquer famous difficult problems" the primary goal or product showcase. He believes this undermines the mechanisms of understanding, teaching, collaboration, and open exploration upon which the mathematical community relies.

Tao pointed out that in traditional mathematics, breaking through a long-standing conjecture is not just about "getting the answer": authors give talks, attend seminars, and exchange ideas with peers, after which proofs are simplified, explained, incorporated into textbooks, and spawn subsequent problems, collaborators, and new research directions.

In contrast, the current approach of companies like OpenAI often involves prompters driving AI to solve problems autonomously; once the goal is "solved," subsequent understanding, reporting, peer discussion, and field building rarely occur. Tao believes that publishers may not even be able to sufficiently explain the AI's output, answer questions, or interact with the field.

He describes this situation as "proof indigestion" in the mathematical community: AI can rapidly generate propositions, proofs, and counterexamples, but humans cannot verify, understand, write, teach, and absorb them fast enough, resulting in a large number of "proofs that no one can digest."

He is particularly concerned that OpenAI treats Millennium Prize Problems such as the Navier–Stokes equations as benchmarks for model capability. In his view, this turns "how many problems solved, and how quickly" into metrics for measuring "understanding and insight"; but speed and quantity alone do not equate to mathematical understanding.

Tao emphasizes that once a problem is publicly "solved," it can hardly be restored to an "unsolved" state. Even if people later want to find different paths or extract new methods from them, merely knowing that an answer exists will "contaminate" this exploration process.

Therefore, he criticizes this as an unsustainable large-scale "harvesting": treating open problems as resources that can be consumed in bulk, which will ultimately make the entire mathematical field less fertile than under traditional research methods.

IT Home Note: Terence Tao is one of the most renowned contemporary mathematicians, a professor of mathematics at the University of California, Los Angeles (UCLA), and a recipient of the 2006 Fields Medal; he is often referred to as the "Mozart of Mathematics."