Birch and Swinnerton-Dyer “Solved Before 2045?” odds jump 38 points on Kalshi after OpenAI’s math claim. A contract asking whether the Birch and Swinnerton-Dyer conjecture will be the next Millennium Prize Problem solved before 2045 traded 100% of its all-time volume in a single session on September 14, 2026, with the implied probability of “yes” sitting at 38%. By contrast, Polymarket’s equivalent BSD-adjacent market logged only $8,907 in total trading volume over the same September 2026 window, underscoring just how concentrated this particular frenzy has been on Kalshi. The move follows OpenAI’s September 8 claim of a result on a different Millennium Problem, Navier-Stokes; a September 11 follow-up in which OpenAI told The New York Times it had made “substantial progress on another Millennium Prize problem” without naming which one; and a wave of unverified social-media rumors that AI labs are circling the remaining open problems. As Tech Insider tracked the market through September 2026, the swing landed only about seven months after Harvard mathematician Barry Mazur delivered a dedicated lecture on the conjecture at Harvard’s Center of Mathematical Sciences and Applications (CMSA) on February 4, 2026, a reminder that BSD has stayed a live research topic among leading number theorists well before any AI lab entered the conversation. No breakthrough on Birch and Swinnerton-Dyer has been confirmed by the Clay Mathematics Institute or the wider math community, and OpenAI’s later October 7, 2026 claim that an unreleased model had solved 372 mathematical problems, backed by published manuscripts and supporting material, has not changed that.
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Timeline: how the rumor snowballed
- September 8, 2026 — OpenAI claims an internal system produced a Lean-checked result on the Navier-Stokes existence and smoothness problem; the Clay Mathematics Institute does not accept the claim and still lists Navier-Stokes as unsolved.
- September 9, 2026 — Unverified posts on X claim the Hodge conjecture is “very close to being verified by OpenAI” and that OpenAI or Anthropic is also close on Birch and Swinnerton-Dyer; the BSD claim traces back to a single user’s prediction, not a lab statement.
- September 11, 2026 — OpenAI tells The New York Times it has made “substantial progress on another Millennium Prize problem,” without naming which one.
- September 14, 2026 — Kalshi’s BSD contract jumps roughly 38 points in 24 hours to 38% implied probability, trading 100% of its all-time volume in a single session.
- September 21–25, 2026 — The Clay Mathematics Institute held a previously scheduled BSD workshop at the University of Oxford.
What the Kalshi market is asking
The contract in question, listed on the CFTC-regulated exchange Kalshi under the ticker KXMILLENNIUMNEXT-45, asks a narrow question: will the Birch and Swinnerton-Dyer conjecture (BSD) be the next Millennium Prize Problem to be solved, before 2045? That framing bundles two conditions. First, BSD has to be resolved. Second, it has to be resolved before any of the other currently open Millennium Problems, and inside the roughly 19-year window the market defines.
The Millennium Prize Problems are seven questions named by the Clay Mathematics Institute in 2000, each carrying a $1 million reward. Only one, the Poincaré conjecture, has been resolved and certified, by Grigori Perelman. BSD, which links the number of rational solutions on an elliptic curve to the behavior of an associated L-function, is widely regarded as one of the hardest of the remaining six. For a primer on how a yes/no contract like this converts to a percentage, see our explainer on implied probability and our guide to how prediction markets work.
The odds as of September 14, 2026, and what they imply
As of September 14, 2026, the market priced “yes” at 38% implied probability, according to Kalshi data tracked by Tech Insider throughout September 2026. That number climbed roughly 38 percentage points in just 24 hours, per the same Tech Insider tracking, effectively from a low single-digit base to its current level, on volume equal to 100% of the contract’s all-time turnover. In plain terms, almost everyone who has ever traded this market did so in one day, and the crowd repriced BSD from “highly unlikely to be next” to “better than one-in-three.” Polymarket, for comparison, saw its own BSD-related market attract just $8,907 in volume across all of September 2026, a fraction of the activity Kalshi’s contract generated in a single session.
A 38% reading does not mean the conjecture is 38% solved. It means the marginal trader is willing to pay 38 cents for a contract that pays $1 if BSD is the next Millennium Problem resolved before 2045. Because the move happened on a sentiment shock rather than a certified result, the figure is best read as a measure of attention and speculation, not mathematical consensus.
What actually moved the market
The trigger was not a BSD result. On September 8, 2026, OpenAI published a claim that an internal system had produced a result on the Navier-Stokes existence and smoothness problem, a separate Millennium Problem. OpenAI said the work took about 88 hours and used thousands of AI agents running concurrently, and that the argument was formally checked in the Lean proof assistant. The company stated it does not intend to claim the $1 million prize. Coverage from Nature, CNN and Quanta Magazine documented the announcement and its many caveats.
The most important caveat: the Clay Mathematics Institute has not accepted the result and still lists Navier-Stokes as unsolved. Reporting noted that the proof relies on a smooth external force, a route the written problem statement permits but that most working mathematicians exclude from the version of the question they care about. In other words, even the confirmed news is contested. That is the event the BSD market is reacting to, one step removed.
The rumor that did the rest
The jump from “OpenAI touched one Millennium Problem” to “BSD might be next” was driven mostly by social media, then amplified by OpenAI itself without ever being confirmed. Around September 9, posts on X claimed the Hodge conjecture was “very close to being verified by OpenAI” and that either OpenAI or Anthropic was also close on Birch and Swinnerton-Dyer. One widely shared post framed it as a race between the two labs to “speedrun” the problems ahead of potential IPOs. Two days later, on September 11, OpenAI told The New York Times it had made “substantial progress on another Millennium Prize problem,” without naming it — a statement that landed, for an already primed audience, like confirmation of the BSD rumor. It was not: the specific claim that BSD is the “other” problem still traces back to social-media speculation, not to any named announcement from OpenAI or Anthropic.
None of the remaining Millennium Problems has been certified solved. There is no named paper, no Lean artifact, and no lab confirmation that BSD specifically is the problem OpenAI referenced on September 11. Fact-checking coverage in September 2026 explicitly labeled the BSD chatter an “unverified rumor,” and the Clay Mathematics Institute’s official overview continues to list BSD as open. Traders repricing on this information are betting on the capability frontier of AI math and on a guessing game about an unnamed OpenAI statement, not on any hard progress specific to elliptic curves.
Who and what is involved
Several real names anchor the story, including Harvard mathematician Barry Mazur, who delivered a lecture on the Birch and Swinnerton-Dyer conjecture at Harvard’s Center of Mathematical Sciences and Applications on February 4, 2026, months before the Kalshi frenzy began. NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had been working on fluid-dynamics problems using large language models, including OpenAI’s Codex. Per TechCrunch, Buckmaster publicly accused OpenAI of aggressive conduct around priority and credit on the Navier-Stokes work; OpenAI said an internal review found that Buckmaster’s Codex prompts could not have influenced its system. OpenAI researcher Sébastien Bubeck features in Buckmaster’s account. Fields Medalist Terence Tao was among mathematicians expressing caution about the framing.
The BSD conjecture itself is named for Bryan Birch and Peter Swinnerton-Dyer, who formulated it from computer calculations in the 1960s. That AI-versus-human credit dispute, more than any equation, is what pulled retail and speculative attention toward the whole Millennium Problem category, and by extension toward this Kalshi contract.
What the math actually says
On the substance, BSD remains firmly open, a point underscored just months before the Kalshi frenzy when Harvard mathematician Barry Mazur delivered a dedicated lecture on the conjecture at Harvard’s Center of Mathematical Sciences and Applications on February 4, 2026, as part of ongoing scholarly engagement with the problem that predates any AI claim entirely. Proofs exist only in special cases, broadly speaking curves of analytic rank 0 or 1, and there is no proof covering curves of higher rank. A recent expository overview of the conjecture and current survey literature both stress that the field is very far from a general proof. Numerical verification for many individual curves, including anything an AI system might compute, is evidence, not a universal theorem. The gap between “checks out for millions of curves” and “proved for all curves” is the entire problem.
A snapshot of the Millennium Problems
| Millennium Problem | Status (Sept 14, 2026) | AI angle in the news |
|---|---|---|
| Poincaré conjecture | Solved and certified (Perelman) | Predates the current AI cycle |
| Navier-Stokes | OpenAI claim; not accepted by Clay | Claimed result, under scrutiny |
| Birch and Swinnerton-Dyer | Open | Rumored target of OpenAI’s unnamed Sept. 11 claim |
| Hodge conjecture | Open | Unverified rumor of lab progress |
| Riemann hypothesis | Open | No credible AI claim |
| P versus NP | Open | No credible AI claim |
| Yang-Mills and mass gap | Open | No credible AI claim |
The Clay workshop adds signal, not a proof
There is one piece of genuine, scheduled news in the mix. The Clay Mathematics Institute held a workshop titled “The Birch and Swinnerton-Dyer Conjecture and Related Problems: Recent Results,” which ran September 21 to 25, 2026, at the University of Oxford and was organized by Chris Skinner of Princeton and Wei Zhang of MIT. The agenda covers generalizations to abelian varieties, rank questions, computational work, results over function fields, and arithmetic statistics.
Read carefully, the framing cuts against the hype. A workshop on “recent results towards the conjecture” is, by definition, a gathering about a problem the community still considers open. It signals steady, incremental progress in special cases and related structures, not an imminent all-curves proof. For a market pricing a resolution before 2045, that is mildly supportive of the long-run “yes,” and firmly against the idea that a solution has already arrived.
Why tech and finance readers should care
This episode is a clean case study in how modern prediction markets absorb a sentiment shock. A confirmed-but-contested AI result on one problem, plus an unnamed OpenAI tease and unverified rumors about adjacent problems, moved real money on a contract whose underlying fact did not change at all, even as Tech Insider’s own September 2026 tracking of the 38%, 38-point swing shows just how fast that repricing happened. Notably, that reaction has so far been almost entirely a Kalshi phenomenon: Polymarket’s parallel BSD market drew barely $8,907 in September 2026 trading, suggesting the sentiment shock hit one regulated US venue far harder than its offshore counterpart. That dynamic mirrors what we have seen in other AI-adjacent markets, including contracts on AI-related outcomes on Manifold, and it sits against a backdrop of active debate over the pace of AI, captured in reporting on whether OpenAI and Anthropic should slow development.
For traders, the practical lesson is source discipline. The confirmed inputs here — an OpenAI claim on Navier-Stokes and an unnamed “another Millennium Problem” tease to The New York Times — are not the same as the traded proposition (BSD next before 2045), and the bridge between them is a viral guess. Kalshi, as a US regulated venue, tends to attract this kind of event-driven speculation, and the September 2026 numbers make the split explicit: Kalshi’s BSD contract burned through 100% of its all-time volume in a day while Polymarket’s comparable market managed only $8,907 over the whole month. Our Kalshi review and Kalshi versus Polymarket comparison cover how these contracts settle and where they are available.
What to watch next
Three things could reprice this market again. First, any official statement from the Clay Mathematics Institute, whether accepting or rejecting the Navier-Stokes claim, would recalibrate how credible AI-driven Millennium results look overall. Second, OpenAI naming the “other” Millennium Problem behind its September 11 statement, or any named preprint or Lean-checked artifact specifically on BSD, would move the story from rumor to evidence; neither exists as of today. Third, the Oxford workshop, underway now through September 25, could surface concrete partial results that shift expert opinion at the margin. Absent those, the current 38% reflects attention decaying back toward fundamentals.
FAQ
Has Birch and Swinnerton-Dyer been solved?
No. As of September 14, 2026, the Clay Mathematics Institute lists BSD as open. Proofs exist only for special cases (analytic rank 0 and 1), and there is no general proof.
Did an AI lab prove BSD?
No. OpenAI told The New York Times on September 11, 2026, that it had made “substantial progress on another Millennium Prize problem,” but did not name BSD. The specific claim that BSD is that problem is an unverified social-media rumor traced to a single prediction, with no named paper, no Lean artifact, and no lab confirmation.
What did OpenAI actually claim?
A result on the separate Navier-Stokes problem, announced September 8, 2026, formally checked in Lean; the Clay Institute has not accepted it and still lists that problem as unsolved. Three days later, on September 11, OpenAI told The New York Times it had made “substantial progress on another Millennium Prize problem” without naming which one.
Why did the Kalshi odds jump 38 points?
Attention spillover from the September 8 Navier-Stokes news, OpenAI’s vaguer September 11 statement about “another” Millennium Problem, the resulting BSD-specific rumors, and a Clay Institute workshop that began September 21. The underlying mathematical status of BSD did not change.
What would count as BSD being solved?
A general proof covering elliptic curves of all ranks, accepted by the mathematical community and certified by Clay. Numerical checks on many curves, including AI-computed ones, do not qualify.
The Bottom Line
Sources
- Kalshi — Will Birch and Swinnerton-Dyer be solved next before 2045?
- Nature — OpenAI claims huge maths breakthrough on a famed Millennium Problem
- CNN Business — OpenAI says it has solved one of math’s Millennium Problems
- Quanta Magazine — AI has solved one of math’s $1 million Millennium Prize Problems
- TechCrunch — OpenAI fought dirty on career-making math problem, says NYU mathematician
- Clay Mathematics Institute — BSD and Related Problems workshop, Sept 21-25, 2026
- Wikipedia — Birch and Swinnerton-Dyer conjecture
- The New York Times — OpenAI statement on “substantial progress on another Millennium Prize problem,” Sept. 11, 2026
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