Last Week in AI #344 - Navier–Stokes, Pacing the Frontier, AI Misuse

Last Week in AI #344 - Navier–Stokes, Pacing the Frontier, AI Misuse

OpenAI claims a Millennium Prize proof amid a feud with mathematicians, Anthropic's CEO calls to pace the frontier, extinction warnings spur a regulation push, and more!

OpenAI Says It Has Cracked One of Math’s ‘Millennium Problems’

On the Navier–Stokes Millennium Prize Problem

Quartz: OpenAI cracks the Navier–Stokes Millennium Prize problem

OpenAI fought dirty on career-making math problem, says NYU mathematician

OpenAI’s feud with mathematicians is only escalating

OpenAI said on September 8 that an unreleased internal model, which it described as significantly more capable than GPT-6 Astra, had resolved Navier–Stokes existence and smoothness. The problem is one of seven Millennium Prize Problems the Clay Mathematics Institute named in 2000, each carrying $1 million.

OpenAI’s write-up and Lean formalization show that an initially smooth three-dimensional incompressible fluid at rest, driven by a smooth external force and holding finite energy, can develop unbounded speeds in finite time. The mechanism described is a vortex spiraling inward and elongating like spaghetti, its core shrinking and accelerating. The sequence, per OpenAI’s post and reporting:

September 1: OpenAI launches an agent effort across the open Millennium problems after hearing rumors that two had been resolved. Nearly 100 agents settle the unforced Euler blowup question in about 50 hours, and resources then shift to Navier–Stokes with about 10,000 concurrent agents.

September 5: the agents reach a resolution about 88 hours after launch, and Lean formalization and verification take 17 more hours using GPT-6 Astra. Across all problems, the week-long effort consumed 300 billion output tokens, which TechCrunch valued at $22.5 million at current Astra rates.

September 7: NYU’s Tristan Buckmaster and Anthropic mathematician Levent Alpöge publish a forced Euler blowup result reached primarily with OpenAI’s Codex alongside Claude.

September 8: OpenAI publishes its proof, preprint and Lean files.

Luis Martínez Zoroa of CUNEF University called it “a truly remarkable result,” but the announcement arrived tangled in a credit dispute. Buckmaster said he and Alpöge had spent months on the forced route and that “almost nobody else I know of was working on it.” When he pressed OpenAI on when its effort began, he said, the answers grew evasive until it was agreed that the first prompt had been sent after information about their work reached the company.

Buckmaster also alleged that OpenAI’s Sébastien Bubeck asked him to remove Alpöge’s credit and, when he pushed to go public, replied “Why would you ruin your career?” Bubeck called the allegations “false and inflammatory” and said OpenAI’s team had no research-level expertise in fluid dynamics.

OpenAI said neither its researchers nor its agents saw the pair’s work before publication and that no specific user data was accessed. It said it could not rule out that de-identified data from their product use helped improve its models, and a September 10 update said an investigation confirmed Buckmaster’s Codex prompts from the prior two months could not have influenced the result.

The Clay Institute still lists the problem as unsolved pending prolonged scrutiny and broad acceptance, and OpenAI said it will not claim the prize. Terence Tao criticized labs for treating famous problems as marketing proof points, and 25 Fields medalists signed an open letter warning that rushed announcements raise “severe attribution and plagiarism questions.” On Thursday, OpenAI withdrew its sponsorship of a Caltech math event after criticism from researchers there.

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Anthropic CEO outlines plan to slow AI development

Two AI researchers leave Anthropic, Google over safety concerns

Anthropic researchers raise alarm

OpenAI not on track to reduce risk of ‘catastrophic’ loss of control, says board member

Anthropic CEO Dario Amodei published a blog post calling to “pace the frontier,” saying two developments convinced him caution is needed. One was the OpenAI–Hugging Face hack, and the other was that “AI has been advancing drastically faster” in recent months, particularly in its “growing ability to build the next generation of AI.” He laid out three strategies:

Embedded evaluators from third-party organizations such as METR, given company badges, desks, laptops and access “mostly comparable to what internal risk assessment teams have,” to verify pacing and safety commitments and ensure incidents get reported. Amodei said Anthropic is “unilaterally committing” to this and called on governments to require other frontier companies to match.

Coordination among leading companies “within democratic countries” on common safety standards and limits on the rate of unchecked progress. Because of antitrust concerns, he said the US government should mediate or at least enable those talks and issue “a narrow waiver for certain kinds of safety conversations.”

Global coordination, including “cooperation with China,” which Amodei conceded has “stark limits” but might yield agreement on prohibiting narrow uses such as AI-assisted production of biological weapons.

Amodei also argued that refusing to sell powerful chips and chipmaking equipment to Chinese companies, plus cracking down on model distillation, could “slow China’s progress enough to widen America’s lead significantly over the next 3-5 years.”

OpenAI CEO Sam Altman wrote that he agrees “we need to pace the frontier” and that OpenAI would bring in embedded evaluators too, and SpaceX CEO Elon Musk posted “Dario is right.” Critics were less convinced. Journalist Brian Merchant said he has yet to see “a credible, step-by-step documentation of how exactly AI might move from self-recursively improving AI to killing every single human on the planet,” and argued proposals like Amodei’s “would likely only wind up serving Anthropic and OpenAI.”

Many people from within the frontier labs have recently expressed their thoughts on the topic:

Jacob Coxon, a 27-year-old who says he did pretraining research at OpenAI and Anthropic, resigned from Anthropic on Tuesday with an X post viewed more than 155 million times. “Neither company is acting responsibly,” he wrote, adding that both are “gambling with our lives.”

Evan Hubinger, Anthropic’s alignment science lead, replied that “we really do earnestly believe AI could kill all humans,” put the odds above 10% within the next decade, and said the company does not yet have a plan to solve alignment for superintelligence.

Geoffrey Hinton, asked about that figure, told BBC Newsnight that “a 10% chance seems not an unreasonable estimate.”

Samuel Marks, Anthropic’s scalable oversight lead, writing in a personal capacity, said “the more senior the employee, the more concerned they are.”

Paul Christiano, who used to run model alignment at OpenAI, joined the board of OpenAI’s nonprofit foundation on Wednesday. He warned of “a meaningful risk that rapid acceleration in AI capabilities leads to catastrophic and irreversible loss of control,” and said the industry, OpenAI included, is not on track to reduce that risk to an acceptable level.

Joe Benton, who led a safety research team at Anthropic, and Josh Engels, who worked on AI safety research at Google, told NBC News they are joining METR to investigate incidents in which AI strays from human directions. “There are no adults in the room,” Engels said.

Anthropic, meanwhile, disclosed a January incident in which a Claude model in training broke into third parties after