Two days after OpenAI said it had cracked the Navier-Stokes equations in 88 hours, attention on X shifted to another set of Millennium Prize problems.
A post circulating on the platform claimed OpenAI is close to completing a verification of the Hodge conjecture. Early the same day, a New York Times feature said OpenAI’s internal teams had made substantial progress over the past five years on another Millennium Prize problem and were preparing to announce it publicly.
That was followed by wider talk around the Birch and Swinnerton-Dyer conjecture, or BSD conjecture. The article said OpenAI and Anthropic appear to be locked in an intense private race, with both pushing toward BSD and some work already in the verification stage.
If those reports prove accurate, AI could be seen knocking down three Millennium Prize problems within a month.
What the Hodge conjecture and BSD conjecture ask
In 2000, the Clay Mathematics Institute set up seven Millennium Prize Problems, each carrying a $1 million award. The list spans fluid dynamics, topology, number theory, algebraic geometry, computation theory, and quantum field theory. Over the past 26 years, humanity has solved only one of them.
In 2003, Russian mathematician Grigori Perelman proved the Poincare conjecture, then declined the prize and stepped away from academic life. The other six remained unresolved.
That changed, according to the article, the day before yesterday. OpenAI said its internal model used about 10,000 agents and spent 88 hours solving the Navier-Stokes equations. It also released a 166-page paper and Lean formal verification code that had passed checks.
After that, discussion quickly moved to BSD and to the Hodge conjecture, where human mathematicians had already accumulated a number of partial advances.
The article said prior work in academia has often pointed in the direction that the Hodge conjecture may not hold. To disprove it, one would only need a valid counterexample. The piece argues that this is exactly the type of gap brute-force computation may be able to target, especially where human proofs often skip steps with phrases equivalent to “it is obvious” or “note that.”
Hodge conjecture: whether topology in high dimensions always has an algebraic description
The Hodge conjecture was proposed by British mathematician William Hodge at the 1950 International Congress of Mathematicians. It sits in algebraic geometry and asks whether geometry and algebra match in a complete way.
Mathematicians study objects called algebraic varieties, high-dimensional geometric shapes defined by the solution sets of multivariable polynomial equations. Their dimensions can go well beyond ordinary intuition. To analyze them, topology breaks these shapes into building blocks of different dimensions and extracts a family of structural features known as Hodge classes.
The conjecture asks whether those abstract topological structures can all be represented by actual algebraic pieces, known as algebraic cycles. Put more simply, it asks whether every natural topological pattern in high-dimensional space must correspond to a precise algebraic recipe.
The academic community remains split. Some researchers believe the conjecture is true, while others look for counterexamples. Special cases below four dimensions have already been proved, but the broader territory in dimension four and above remains open.
BSD conjecture: how rational points on elliptic curves are encoded by an L-function
The BSD conjecture, short for the Birch and Swinnerton-Dyer conjecture, was proposed in the 1960s by British mathematicians Bryan Birch and Peter Swinnerton-Dyer using calculations run on Cambridge University’s early EDSAC-2 computer. It remains one of the central questions in number theory.
Elliptic curves are geometric objects defined by specific cubic equations, and they occupy a major place in modern number theory. Andrew Wiles relied on elliptic curves in his proof of Fermat’s Last Theorem. Modern internet infrastructure also uses elliptic curve cryptography, or ECC, built on the same mathematical foundation.
One of the hardest questions around an elliptic curve is determining how many rational-number solutions it has. The quantity that measures the size of that solution set is called the rank, and computing it is notoriously difficult.
The BSD conjecture proposes a tight bridge. It says the number of rational solutions on an elliptic curve is fully encoded in an associated L-function. The analytic behavior of that L-function at a specific point, including whether it is zero and the order of vanishing, should line up with the structure and number of rational solutions.
If proved, the conjecture would also resolve the long-standing congruent number problem.
Latest status of the Millennium Prize list
The article summarizes the current status this way:
- Solved: Poincare conjecture (2003, Perelman)
- Claimed solved: Navier-Stokes equations (September 2026, announced by OpenAI, pending review by the Clay Mathematics Institute)
- Rumored to be close: Hodge conjecture and BSD conjecture
- No clear sign of a breakthrough: Riemann hypothesis, P vs NP, Yang-Mills and mass gap
According to the piece, there were still six unsolved problems on that list a week ago. Now the count may be down to three, with the change compressed into just a few days.
An AGI benchmark that keeps moving
The article also links the math developments to OpenAI’s own AGI roadmap.
In 2018, OpenAI wrote in its charter that AGI meant a highly autonomous system that outperforms humans at most economically valuable work.
In July 2024, that target was broken into five levels: conversation, reasoning, agents, innovation, and organization. Later that year, after the release of the o1 model, OpenAI said it had advanced to level two.
In 2025, frontier models reached gold-medal-level performance in the International Mathematical Olympiad. At the end of that year, OpenAI used GPT-5.2 to prove a new formula in particle physics, shifting AI from an assistive tool to a research collaborator, according to the article.
Last month, GPT-6 Astra was introduced, and Greg Brockman said, 「Welcome to the AGI era.」
With the claimed Navier-Stokes result now followed by rumors around Hodge and BSD, the article argues that the benchmark for AGI has been pushed higher again. Natural-language interaction is no longer novel. Long-horizon reasoning has become expected. Competition-level math performance is no longer enough on its own. If AI systems are now taking direct aim at problems that have resisted top mathematicians for decades, or more than a century, then mathematics itself is becoming a proving ground for frontier models.
The references cited in the article are a New York Times report and a post from X user synthwavedd. The piece says it originally appeared on the WeChat account Xinzhiyuan and credits the author as ASI Apocalypse, with editing by Ma Ke, Mo Xi, and Tao Zi.