OpenAI model finds Navier-Stokes answer amid credit and privacy questions

OpenAI model finds Navier-Stokes answer amid credit and privacy questions

2 min read•Sep 13, 2026•
Ryan O'Connor
Ryan O'Connor

OpenAI announced that an unreleased AI model found an answer to the Navier-Stokes Millennium Prize problem, first reported by Singularityhub. The equations model fluids such as water and air, and some mathematicians have raised questions about credit and private work while prize conditions bar any award until at least two years after publication of a potential solution.

These equations underpin modern science and engineering. The question is whether fluid swirls can shift their energy into smaller, faster swirls, accelerating until the equations produce a blow-up in speed, also known as a singularity; OpenAI’s answer is yes under certain conditions.

The problem is one of seven Millennium Prize puzzles carrying million-dollar rewards, and only one had been solved before the announcement. OpenAI deployed a swarm of 10,000 AI agents running a new experimental model, using millions of dollars’ worth of computing power over a few days.

The model produced a solution in 88 hours, with verification taking another 17; the American Mathematical Society called the work the “final steps” of the solution process. The result built on work by several human mathematicians.

Tristan Buckmaster, a New York University mathematician, said he and Anthropic staffer Levent Alpöge had been using OpenAI’s publicly available models and pursuing a similar line of thinking. Buckmaster said he asked whether their data had been used by OpenAI’s model and received no answer; he also said OpenAI offered collaboration if Alpöge’s name was removed because of his Anthropic affiliation. OpenAI denies that claim.

German mathematician Andreas Thom suggested that OpenAI’s models were using unpublished human work and presenting it as AI-generated. Terence Tao has raised concerns about the indiscriminate use of powerful solution-extraction tools to achieve immediate short-term goals at the expense of broader understanding.

OpenAI insists that no specific user data was accessed by its researchers, but questions remain about whether the model was trained on Buckmaster and Alpöge’s private work. Companies and individuals around the world will now be re-examining how much they can trust OpenAI and other AI companies to handle their private and business data.

The model’s 88-hour result sits alongside a prize process that requires at least two years after publication of a potential solution before an award. For now, the Navier-Stokes problem is still officially unsolved.

Arizona appeals court vacates manslaughter sentence after AI video

An Arizona appeals court vacated the 10.5-year sentence of Gabriel Horcasitas while upholding his manslaughter conviction, first reported by Nytimes. The case returns to Maricopa County Superior Court for resentencing without the video, after judges found that it presented scripted statements as if the victim himself were speaking in court.

The three-judge panel said the video generated a likeness of Christopher Pelkey’s voice and appearance but did not reflect actual events. It found that allowing and relying on the video made the sentencing fundamentally unfair, and noted that no prior Arizona case had addressed the admissibility of such a depiction at sentencing.

The judges said a victim’s right to speak cannot override a defendant’s right to be sentenced on accurate, reliable information. They said the video collapsed the distinction between the family’s belief about what Pelkey would have said and Pelkey’s own voice and opinions.

The ruling distinguishes family members speaking about Pelkey from a generated likeness that appeared to speak for him.

Pelkey’s sister, Stacey Wales, presented the video during Horcasitas’s sentencing alongside victim-impact statements from family and friends. Wales wrote the script and said her husband and the couple’s longtime business partner helped create the video using Pelkey’s voice from a YouTube video and his face and torso from a funeral-service poster.

Judge Todd F. Lang praised the video as genuine, then imposed the maximum sentence of 10.5 years, more than the nine years prosecutors had sought.

Wales said nobody intended to make the court believe Pelkey was alive or that he had recorded the video before his death. She said she disagreed with the ruling and argued that families use slide shows, collages, hypothetical conversations and poetry to convey grief.

Wales compared the AI video with photography, saying it took 15 years of landmark cases around the 1860s before photography was widely accepted in courts.

The case returns to Maricopa County Superior Court for a new sentencing hearing without the AI-generated video.