OpenAI's 719 mathematics papers came from testing its opposition advisers

OpenAI released 719 mathematical papers causing controversy, experts call for a stop to testing advanced mathematical problems on proprietary models.

On October 6, OpenAI uploaded 719 mathematical papers generated from its unpublished internal model to GitHub. However, just this week, its own advisory group asked major laboratories to stop testing advanced mathematical problems on proprietary models.

Based on more than 600 survey responses, the Mathematics and Artificial Intelligence Advisory Group at the Institute for Advanced Study in Princeton, New Jersey issued guidance on September 29. "The first thing we want to clarify is that we disagree with this approach and ask all parties to stop testing high-level mathematical problems on proprietary models," the group made clear in its statement.

The document also warns that the use of private internal models may lead to a "dual-track system" in the industry, in which a few laboratories quickly surpass other research teams with closed resources, thus undermining the level playing field in the field.

Background and response

OpenAI stated in its code base that as part of model development, the company will test models on public research questions. As existing mathematical benchmarks become saturated, the scope of these tests has expanded. OpenAI claims to have communicated with the advisory group and published relevant content after referring to its recommendations. However, in a statement issued on October 6, the advisory group emphasized that its advisory role does not represent recognition of OpenAI's process to obtain these results.

The final ruling on compliance has been left to the broader mathematical community.

Technical Details and Formal Verification

OpenAI classified these 719 papers into 372 mathematical families, each family built around a major result and its associated proof. The company provides about 4,000 questions for its proprietary model, and each result requires about three hours of thought calculations by ChatGPT Pro on average.

The advisory group recommended that AI laboratories publish the model name, prompts, simplified thought chain, time and calculation cost for each result. Currently, OpenAI has published 10 inference summaries, and about 42% of the main results are accompanied by Lean's formal proof.

Lean is a programming language that can be used for computer verification and certification. If the code is compiled successfully, it only means that the formal statement is logically valid, but this does not mean that the code is completely consistent with the written argument.

Potential risks and academic doubts

Alexander Bastounis, Fabian Circelli and Anders C. Hansen explores these gaps in depth in a paper published on October 6. They found that the claims made in the Navier-Stokes equations paper written by OpenAI were stronger than what its Lean code actually proved, with one estimate even changing the order of the input derivative.

The author also demonstrated at OpenAI's Euler that similar mistranslation phenomena were detected. "OpenAI's written certificates and other automated formal Lean certificates should not be blindly trusted without going through the same peer review process and rigorous review as other certificates," they wrote.

In addition, OpenAI announced the results of the Navier-Stokes equation on September 8. According to Cryptopolitan, New York University mathematician Tristan Buckmaster questioned the description of the minimum human input involved in the work. In response, the company promises to provide financial support for seminars, conferences and special projects related to major AI achievements.

Academic response

On October 6, the famous mathematician Tao Zhexuan issued an article pointing out that many AI prompt engineers often lose interest in the field after solving problems. He wrote that many people were unable to answer questions or speak about the results. It is worth noting that his post did not name OpenAI.

Previously, Cryptopolitan reported in September that the company said its consultants had no right to interfere with the pace of its research.