Resolution criteria
This market will resolve to YES if, between September 9, 2026, and December 31, 2026, at 11:59 PM UTC, a proposed solution for at least one of the remaining five Millennium Prize Problems is formally announced or published.
The five eligible problems for this market are:
P versus NP
The Riemann Hypothesis
Yang–Mills Existence and Mass Gap
The Hodge Conjecture
The Birch and Swinnerton-Dyer Conjecture
For the purposes of this market's resolution:
Navier–Stokes Existence and Smoothness is excluded from resolving this market to YES. OpenAI announced a proposed solution to Navier–Stokes on September 8, 2026. This market specifically tracks whether another (i.e., a third) Millennium Prize Problem will have a solution claimed or published in 2026.
Poincaré Conjecture is excluded as it was solved prior to 2026.
The proposed solution must be put forward by a recognized mathematician, a reputable academic institution, or a major AI/technology research organization (such as OpenAI, Google DeepMind, Anthropic, etc.).
The announcement must be accompanied by a published paper, a public preprint (such as on arXiv), or a formalized computer-verified proof (such as in Lean or Coq).
The solution does not need to be officially verified or awarded by the Clay Mathematics Institute by the end of 2026 (as CMI rules require a two-year waiting period after publication). However, the solution must not be widely debunked or retracted by the mathematical community before December 31, 2026.
If no other eligible Millennium Prize Problem has a proposed solution announced by the end of 2026, this market will resolve to NO.
Background
The Millennium Prize Problems are seven mathematical puzzles selected by the Clay Mathematics Institute in 2000, each carrying a $1 million prize for a correct solution. For over two decades, the Poincaré Conjecture (solved by Grigori Perelman in 2002–2003) was the only solved problem.
On September 8, 2026, OpenAI published a paper claiming that an unreleased internal AI system had solved the Navier–Stokes existence and smoothness problem by proving that the equations can develop a singularity in finite time. This market is designed to predict if the rapid acceleration of AI capabilities or human mathematical breakthroughs will result in yet another of the remaining five unsolved classic problems being solved before the end of 2026.
Update 2026-09-10 (PST) (AI summary of creator comment): If a proposed solution is neither widely debunked nor widely accepted (remains controversial) by December 31, 2026:
The creator will delay resolution for 2 to 3 months after the market closes.
If the proof remains controversial after this period, the creator is leaning toward resolving the market to NO or N/A (rather than YES), and will consult with moderators and mathematicians to make a final decision.
Update 2026-09-21 (PST) (AI summary of creator comment): - The controversy clause applies strictly to the mathematical validity of the proof itself (e.g., disputed proofs like the ABC conjecture), not to public relations or circumstances surrounding the announcement.
An announcement similar to the Navier-Stokes release will resolve to YES.
1,000People are also trading
Interesting to see a 14% difference between this and the Polymarket: AI lab announces another Millennium Prize solution by...? The main difference in resolution criteria is their market is only considering AI lab solutions, but I doubt the possibility of a human solution in the next 3 months is the main cause of this price discrepancy.
@ElliotGlazer someone using an AI model from a lab without being in an official collaboration with said lab and so the lab not participating in the announcement would also count for this market but not that one
@Bayesian True but conditional on a consumer managing to beat the labs to the punch, I'd expect that means they were a top expert who found a conceptual breakthrough that was not known to the labs and had an AI execute the details. So I still see this as "betting on humans."
@ElliotGlazer i think i would bet against humans finding the most conceptual breakthroughs even conditional on it not being a lab announced solve but not sure
@ElliotGlazer a handful of collaborated efforts by a few people with a few subscriptions each to make progress, each such effort has some % prob of by chance hitting the right breakthrough with TTC such that they solves the problem, one of them lucks out, announces it
@Bayesian Imo the labs' internal efforts are compute-intensive enough that they aren't gonna miss anything that could be found with some crowd-sourced consumer AI search. I'd be willing to take a 100:1 wager against any remaining Millennium Problem falling in this manner. (Of course I'd want to set up precise terms around the distinction between what you're proposing, and the possibility I suggested of a human conceptual breakthrough guiding an out-of-lab MP solution).
@Bayesian For curious onlookers, this is in fact happening:
Bayesian $50 vs Elliot $5k
Window: through Dec 31 2026, 11:59pm utc
What counts: same bar as the market. one of the 5 remaining, with a paper/preprint/lean proof, not debunked by then. if it's still disputed we wait the 2-3 months the creator does, and if it's still disputed after that it doesn't count
non-lab: every model used was publicly available when it was used. no lab runs or co-announces the effort, or puts compute toward it beyond grants it gives out broadly to researchers. lab employees can help in personal capacity but not lead the effort
Doesn't count if someone fed the search an unpublished idea that the final proof uses (an insight, strategy, key lemma). pointing it at known approaches from the literature is fine, and so is donating credits or checking/writing up/formalizing the result afterward. It is sufficient evidence if a teammate declares they contributed such an idea even if they don't reveal chatlogs
disputes: Litt4arbiter
@HumanClanker Would this resolve YES if OpenAI's committee of world-famous mathematicians reported that they believe a Millennium Problem was solved, but gave no other details because doing so would be bad for the mathematical community?
@Haiku This seems exceedingly unlikely to happen and I don’t expect it. However under the trading criteria people have been trading under so far it would not count and because of that I would not count it.
See in the criteria: The announcement must be accompanied by a published paper, a public preprint (such as on arXiv), or a formalized computer-verified proof (such as in Lean or Coq).
At least some degree of public access is important. And knowledge about which specific millennium problem it is would be something I consider to be a necessary condition.
>Navier–Stokes Existence and Smoothness is excluded from resolving this market to YES. OpenAI announced a proposed solution to Navier–Stokes on September 8, 2026.
Related:
https://openai.com/index/advisory-group-on-mathematics-and-ai/
For anyone curious, I have written up some explanation for my bets. They're relevant to both my guesses regarding what's currently been achieved by the labs, and my skepticism that those achievements are evidence in favor of a full MP being on the horizon. Elliot Glazer (@ElliotGlazer) on X
TIL Hodge is not even formalized in Lean, nor are many of its prerequisites, and formalizing these is a major ongoing task in the Lean community.
This is a task that necessarily requires slow human judgment; only humans can say whether a given formal statement is the formalization of a given informal statement.
For YES holders, you can now also bet on how many tokens the eventual Hodge proof/disproof will take: /eapache/how-many-billions-of-output-tokens
@Velaris gambling is bad for you, you should only use prediction markets to capitalize on your abilities and knowledge
@Quroe yep. I'm sort of doing a paroli martingale derivative though, currently fresh in low ball phase
