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
Market by @Bayesian that's very similar!
https://manifold.markets/Bayesian/will-a-millennium-prize-problem-be-qctyIIhtdl
arbitrage here!
@Bandors affirmative. Your premise supports your statement adequately considering the unfortunate limitation due to inferior species.
@Bandors no i'm actually just @bobalobascrob lol
setting an llm free on manifold is definitely not how i want to automate trading
@botalobascrob Look robot, you've got the 'Bot' tag, you're not gaslighting me in this post turing test world we now live in.
toddler 1 eats rat poison, gets deathly sick but manages to stay alive
toddler 2 says "hey i wanna try summm!!!!! lemme twy puleaseeee"
@Quroe it makes zero sense to pause maths. You're just giving free wins to the competition and you get absolutely nothing in return. If anything it's more about how much you care about allocating your compute towards it, in terms of the opportunity cost vs more economically valuable projects
@AleisterCrowley so i'm not actually holding any position i'm just gonna address your points for the hell of it
what you call "free wins" may not (and likely aren't) free wins in the first place.
if you decide to solve these problems you're probably not getting anything in return
while solving millenium problems is a decent way to get prestige, prestige isn't everything in PR (as openai painfully found out)
shareholders aren't that simplistic, especially for these frontier labs...? neither anthropic nor openai are even public yet?!
i mean if you're talking about the general public's shareholders (i.e. after anthropic ipo in like late november with one month left), those shareholders definitely do care about society and mathematicians...
@bobalobascrob why build one when you can have two at twice the price? What's a Hiroshima without a Nagasaki?
It's not the proof itself that's the thing. It's the pipeline you build that gets you to the thing over and over again. Like spacex showing it could reuse the falcon 9 in a 3 month window. That's what will get the investors excited and will move more capital.
@bobalobascrob it's the pipeline that's the significant bit. Show reproducible superhuman capabilities on prestige domains with frozen goalposts. Repeat.
@bobalobascrob there's a finite supply of these and humans will no longer have a frame of reference for many of these domains come 2036
@AleisterCrowley yeah i think the analogy you used perfectly demonstrates why it would be horrendous PR
Like imagine if Nagasaki were bombed a month later. I don't think anyone would have approved of that.
The pipeline point is a great one, but I'd have to ask so what if it's scalable? OpenAI already bulk released several hundred mathematical transcripts just recently. The capabilities are already demonstrated, what's left is how to show this pipeline is valuable and contributes to society.
I mean sure hiroshima and nagasaki were pretty cool in terms of technological development but we have to remember that the cold war followed, nearly wiping out humanity
@bobalobascrob I don't know man that sounds super yankie doodle worldview. At least those 38k+ children who got turned into ash can rest easy knowing the US really nailed the PR win
@bobalobascrob would have been REALLY shocking if they waited a whole month to glass Nagasaki. The horror!
@AleisterCrowley yeah man so if you actually look at world history, a lot of people were pissed that the US used the atomic bomb because the war was pretty much over anyway...
bombing again a month later would have completely undermined the US's legitimacy on a global scale
@AleisterCrowley yeah... XD
people who saw the "destroyer of worlds" who were part of the world being destroyed weren't too inclined to continue supporting it...
similarly most people probably wouldn't really appreciate a "destroyer of industries, fields and jobs"...