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
Has anyone ever run the numbers on intra trading window accuracy of manifold versus polymarket? I know collectively manifold has a fairly unique user base relative to the much larger money markets, and while I'd like to think that might mean less "dumb money" that's probably less accurate than it being the case that lower liquidity means smaller groups of confident people sway the manifold versions of markets in more volatile ways or that the discount value is such that people wait longer to pull their mana versus the money markets?
I imagine people doing more limit orders would lead to more accuracy in general and be more reflective of people's actual confidence levels on here(something I am admittedly often too lazy to do).
For what it's worth I hold a very small yes position that I am slowly pulling from as the trading window shortens, but I would probably be better served and the accuracy and liquidity of the market better served if I did this through limit orders. Which is to say is that the real root of the gaps? Is this a limit order propaganda comment?
@ShaneBo Are these the references you need?
@Quroe Awesome! Thanks for sharing....was not aware of these sources, so I'll definitely dig into them.
However, these seem to cover mostly aggregate outcomes rather than the underlying mechanics driving the differences, which I'm most interested in. Manifold's calibration page notes that they are still looking into how liquidity and slippage affect accuracy(hope they do this soon), and their methodology relies on trade-weighted rather than time-weighted calibration; which naturally obscures the intra-window path. A lot of the case studies are also quite old
But the city calibration page does seem to point to higher intra-window accuracy for real-money markets with the gap narrowing as the window shortens, with that in mind I'm guessing it's mostly a trade friction(liquidity/slippage) problem that drives the differences
"All of these are problems I mentioned in my presentations and grants. I'm now in an unprecedented situation where all the research avenues I had have been solved."
@0xseraphim I'm not looking for a counterparty at the moment. I'm just saying that I don't think that the material shared here is worth my time to check out unless I see some conviction.
@0xseraphim And it seemed like I was on the money. I have no exposure in this market at the moment, but I certainly "bought low and sold high". I have a guaranteed profit, no matter how this market resolves.
@Quroe you're right of course. We should all stay as quiet as possible and act only to move the price. Words have no power here. The invisible hand of the free market has entered me, and I now feel its presence deep inside. Hail Epistemics!
@Quroe if you want a little bit more context here:
I posted the video to steelman the argument that another millenium prize problem won't be solved this year. There seems to be a uniquely negative reaction from the mathematics community that may deter the AI companies from doing a repeat of the navier stokes episode. ALso, @pietrokc indicated to me to stop posting hot takes from people on twitter and actually go to the mathematicians (Hugo Duminil-Copin is recent fields medallist).
Despite this, I think the chances are good that we'll get another millenium prize solution this year. I don't think they're going to stop at hiroshima.
@Quroe Maybe I could have expressed this better through the medium of limit orders? Or maybe I could have expressed this through the medium of interpretative dance? Either way, none of my comments are special snowflakes; and there's lots of people on manifold who have waaay better understanding of the underlying problems than I do.
@BrendanFinan hey we can both interpret the outcome of this conversation as vindicating our own positions! This is a judgement-free and positive-sum zone
@0xseraphim I think a better steelman of why another MP won't be solved this year is that they tried this new model on thousands of problems and the solve rate was ~5%. I don't think OpenAI cares about mathematicians' reactions at all. (I'm sure there are people at OpenAI who do, but they are not the ones making the decisions.)
@0xseraphim Ah, okay, I misinterpreted this. I thought you meant you uploaded the video.
I posted the video to steelman the argument...