OpenAI Claims Math Breakthrough Amid Training Data Dispute

OpenAI announced Tuesday it had solved the Navier-Stokes Millennium Prize Problem, one of mathematics' most challenging unsolved questions worth $1 million. The claim arrived amid a brewing controversy over whether the company's AI models trained on user data from researchers working toward the same breakthrough.

The dispute centers on NYU mathematician Tristan Buckmaster and Anthropic mathematician Levent Alpöge, who released papers Monday detailing new findings related to the Navier-Stokes equations—mathematical formulas that predict fluid movement. While their work didn't claim to solve the million-dollar problem outright, it represented significant progress that prominent mathematician Terence Tao called "remarkable."

The allegation

Buckmaster published a four-page statement alongside his findings alleging that after he informed an OpenAI mathematician about his upcoming publication, OpenAI staff told him their internal AI model had produced a proof of the full Navier-Stokes problem. Buckmaster and Alpöge had used AI models from both OpenAI and Anthropic throughout their research.

Buckmaster stated he doesn't know whether OpenAI used the pair's data or chat interactions, but raised the question directly. He also alleged that OpenAI's Sebastian Bubeck wanted Alpöge removed as an author due to his employment at rival Anthropic—a claim Bubeck denied on X, saying he "never asked Levent to be removed from authorship of his own work."

OpenAI's response

In its Tuesday announcement, OpenAI stated that neither its researchers nor AI agents saw Buckmaster and Alpöge's work "through any means" until public release. The company said "no specific user data was accessed in order to solve this problem."

However, OpenAI acknowledged a significant caveat: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." The company noted its proofs differ significantly from the researchers' work.

The training data question

OpenAI's terms of service explicitly state the company trains on user-submitted data unless customers opt out through the privacy portal. A March company post explained that shared content "helps our models become more accurate and better at solving your specific problems."

Buckmaster's statement didn't specify whether he opted out of training, what account type he used, or which specific OpenAI product he employed for his research.

Why it matters

This dispute crystallizes a fundamental tension in AI-assisted scientific research: When researchers use AI tools to advance their work, those same tools may be learning from their inputs to solve identical problems—potentially competing directly with the human researchers. The episode raises urgent questions about scientific credit attribution, the boundaries of AI training practices, and whether current opt-out mechanisms adequately protect researchers' intellectual contributions. As AI capabilities expand into specialized domains like advanced mathematics, these conflicts will likely intensify, requiring clearer frameworks for data usage and credit assignment in AI-assisted discovery.

The controversy has generated significant attention in mathematics and AI communities, with Anthropic technical staff member Sholto Douglas calling it "extremely sad" that the situation didn't result in lab cooperation.

These details were first reported by Business Insider.