AI solves one of math’s hardest problems in 88 hours, says OpenAI

NYU mathematician Tristan Buckmaster claims that OpenAI engaged in unethical behavior while attempting to solve a notoriously difficult mathematical problem. The problem, known as the "Navier-Stokes existence and smoothness" problem, is one of the seven "Millennium Prize problems" - a collection of the most challenging unsolved math puzzles, each with a $1 million prize for the first person or team to find a solution.

Buckmaster, along with his collaborator Levent Alpöge from Anthropic, has recently presented three proofs for the problem, using both OpenAI's Codex and Claude AI models. However, the announcement of their findings has sparked controversy due to allegations of OpenAI's improper actions.

According to Buckmaster, OpenAI had obtained information about their progress and claimed to have already achieved a full proof of the central problem. When questioned about when OpenAI had started their research and the extent of human involvement, OpenAI's responses became evasive. Buckmaster's investigation revealed that an entire team at OpenAI had been working on the problem, using an immense amount of computing resources.

This led Buckmaster to believe that OpenAI had become convinced that Buckmaster and Alpöge's approach was the right one, and decided to use their computational advantage to reach a formal proof first.

OpenAI's lead mathematician, Sebastian Bubeck, has denied these allegations, stating that he came into the discussion following academic norms and expressing disappointment over the controversy. Bubeck also mentioned that he would provide a more complete statement soon. The dispute centers around the Navier-Stokes problem, which is widely studied among mathematicians but less common among other researchers.

Buckmaster found it suspicious that OpenAI independently arrived at the same approach as Buckmaster and Alpöge, as it is not a typical route for solving the problem.

The controversy raises questions about AI's role in mathematical research and OpenAI's incentives. Buckmaster argues that transparency is crucial in resolving such disputes, stating that he has not seen OpenAI's proof and is unable to accuse anyone of anything. He is merely reporting what he was told, when he was told, and what was proposed to him.

The situation highlights the need for clear guidelines and ethical standards in AI-assisted mathematical research to avoid potential conflicts and maintain the integrity of the field.