Earlier this week, while I was busy losing all my money in what I thought would be the future of finance, OpenAI claimed to have solved another one of mathematics' hardest problems. This time, it was one invented back in the 1850s, when the only program on Earth was a degenerate gambler who I know would have loved Horse Tender. The problem is called Navier-Stokes, and it's a set of equations we've grown to rely on for determining the movement of fluids and gases. But, unlike those other videos you've watched about the movement of fluids and gases, this one's plot is way more interesting. >> Because this is just like crazy drama for us. >> In this video, we'll find out what makes Navier-Stokes so hard, look into whether OpenAI actually solved it, and learn why a math professor at NYU, a mathematician at Anthropic, and Sam Altman are all telling very different stories about what happened on a phone call last Sunday. It is September 11th, 2026, and you're watching The Code Report. Back in the 1800s, a French engineer named Claude-Louis Navier wrote down some equations describing how fluids move. Then, a couple decades later, an Irish mathematician named George Stokes fixed the engineer's work, and eventually they got branded as the Navier-Stokes equations. They're basically force equals mass times acceleration, but for water. The idea is you give the equations the current state of a fluid, like how fast it's moving and how much pressure it's under, and what you'll get back is how that fluid will move a moment later. And for almost 200 years now, engineers have trusted them for some pretty crucial stuff, like forecasting hurricanes, designing airplane wings, and simulating how blood pumps through their meatbag bodies. But, of course, mathematicians don't trust anything until it's proven. And there's one question about these equations that nobody could answer, which in very simple terms is, can they ever break? That question has been so difficult that 26 years ago, the Clay Mathematics Institute made it one of their seven Millennium Prize Problems and put a million-dollar bounty on its head. To claim the money, you either need to prove the equations never break, or show one case where they do break. As you can imagine, there aren't a lot of people who care about that problem, let alone have any chance of solving it. But, someone who does is Tristan Buckmaster, a math professor at NYU who won the Clay Research Award back in 2019 for some work he did on these exact equations. Last year, he teamed up with Levent Alpige, a mathematician who happened to work at Anthropic and in his spare time apparently enjoys working on century-old fluid dynamics problems. Together, the team was making slow but steady progress until mid-August of this year when Levent realized what the company he works for actually does. At that point, they started leaning more heavily on Cod code and Codex for help and their progress took off. The approach they ended up taking was novel but also a bit of a long shot and on August 15th, it paid off when they got a simpler version of Navier-Stokes called the Euler equations to fall apart. It wasn't the million-dollar problem, but it was the closest anyone had ever gotten. Then, as if they had just gotten vaccinated, OpenAI suddenly got very interested in math. In late August, as they were training a new model, they decided to give it every unsolved millennium problem at once to see what would happen. The 10,000 agents and 20 million dollars worth of compute later, they claim to have broken Navier-Stokes. And what do you know, the process they used was the exact novel process that Buckmaster and Alpige had spent the last year working on and throwing into Codex, which brings us to the phone call. On September 3rd, Buckmaster emailed OpenAI to ask what was going on. That Sunday, he got on a call with Sebastian Boubek, the OpenAI researcher running the project. Buckmaster was told all OpenAI did was give the model the problem statement with very little input. Then, as the call went on, it became clear that the whole team worked on it. The prompt was written by Codex and they had only started it a few days earlier when they heard rumors about his work. Buckmaster then questioned whether the model had been trained on his Codex sessions and was told only that it didn't look up user data, but when he pressed on training specifically, according to him, he got no answer. From there, he claims OpenAI laid out two options. The first was that Buckmaster and Alpige could publish their Euler results first, then OpenAI could publish its Navier-Stokes proof and credit Buckmaster as the person who got closest to solving it. The second was that Buckmaster could write the Navier Stokes paper himself, but leaving off Alpagay because he works at Anthropic. And so, Buckmaster did what any gigachat would do, and he refused both options and threatened to go public. Then, according to his statement, Boubacar asked Buckmaster why he'd ruin his career and told him that if he didn't want Boubacar to be nice, then he didn't have to be nice. But, of course, OpenAI has a different story, claiming that they never asked for Alpagay to be removed from his work. And Sam says he believes everyone on their end acted with integrity, and Buckmaster was the only one making threats. So, on Tuesday morning, Buckmaster and Alpagay posted their papers along with a four-page statement describing how it all went down. That afternoon, OpenAI posted their own solution along with a blog post insisting that no user data was accessed, and that the two proofs are significantly different. And that night, Madam Zeroni posted her own statement saying that Sam and Boubacar must carry her up the mountain or OpenAI will be cursed for all of eternity. >> You and your family will be cursed for always and eternity. >> And just yesterday, rumors started circling that OpenAI is very close to verifying another millennium problem, approving that all it takes to change the world is a little elbow grease, 10,000 agents, and $20 million worth of compute. Of course, Terence Tao has the most reasonable take on all this, congratulating Buckmaster and Alpagay on their work, and warning that if the mere rumor of your research can trigger a swarm of agents racing to front-run it, mathematicians will simply stop sharing ideas, which will undo centuries of open science. The lesson here might be to be careful which companies you trust, which is why I host all of my projects on Railway, the sponsor of today's video. They once again refused to waste your time with a full ad, which makes sense for a company that lets you deploy anything with just a few clicks. So, if you want to say thanks, you can try deploying your next project for free with the link below. This has been The Code Report. Thanks for watching, and I will see you in the next one.
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