OpenAI Announces Major Mathematical Breakthrough, Sparking Controversy Among Scholars

OpenAI announced today that it has discovered an AI-generated solution to one of the most significant challenges in mathematics—a 200-year-old equation that characterizes the natural behavior of fluids such as water and air.

This revelation showcases AI’s remarkable potential to advance mathematical understanding. However, it has been overshadowed by allegations from mathematician Tristan Buckmaster, who claims that OpenAI hastily claimed a solution after learning of his and another mathematician’s work on the issue, and also attempted to manipulate who would receive credit for the accomplishment.

The proof relates to the Navier-Stokes equation, one of the unresolved problems listed in the Clay Millennium prizes, each of which is valued at $1 million.

Sebastien Bubeck, a mathematician and AI researcher at OpenAI, stated in a press conference that the company began training a new AI model with enhanced mathematical abilities on August 28.

Upon hearing rumors that Anthropic was making strides toward solving Navier-Stokes, Bubeck noted the company decided to allocate additional resources to address the issue. More than 1,000 agents worked on the problem for over 50 hours before arriving at a solution.

“I thought there had to be some kind of mistake,” Bubeck remarked. “And on Sunday morning, we finalized the solution, Lean-formalized and all.” (Lean is a programming language suitable for formalizing mathematical proofs.)

OpenAI pointed out that solving this equation necessitated significantly greater computing resources than previously dedicated to mathematical problem-solving. The costs associated were “in the millions of dollars,” according to Mark Chen, head of research at OpenAI.

On Monday, Buckmaster of NYU and Levent Alpöge from Anthropic shared documents claiming crucial advances related to the Navier-Stokes problem. They asserted they utilized several AI models, including Claude and Codex, in their research.

Buckmaster also released a statement indicating that he recently discovered OpenAI had recognized his and Alpöge’s efforts and started investing significant resources into the matter. He claimed to have inquired with OpenAI leaders about whether the company accessed the pair’s Codex logs. He alleges he was informed the model “didn’t look up user data,” yet the company did not respond to inquiries about training. He stated that OpenAI made several “proposals,” including one where Buckmaster could publish a paper declaring the Navier-Stokes problem solved by an internal OpenAI model without including Alpöge’s name.

Neither Buckmaster, Alpöge, nor Anthropic offered an immediate comment to WIRED.

During the briefing, Bubeck and other OpenAI leaders rejected claims that the company had reviewed the pair’s Codex prompts to guide their own efforts. “We, whether researchers or agents, did not see any of their work until it was publicly released last night,” he stated.

“I want to be clear that we acknowledge the contributions of Levent Alpöge and Tristan Buckmaster on unforced Euler, and we extend our congratulations to them for this significant achievement. To clarify, we did not utilize their prompt or proof to guide our models or direct our agents,” Bubeck added.

OpenAI expressed a desire to acknowledge Alpöge and Buckmaster’s earlier efforts. However, Ven Chandrasekaran, a mathematician at the company, highlighted that their solution differed significantly in nature from that produced by OpenAI’s model.

The debate over credit for resolving one of mathematics’ most significant challenges is likely to continue. As AI takes on a greater share of the work involved in finding proofs, such disputes might become more commonplace.

This is a developing story. Please check back for updates.