Millennium Prize Problems Unsolved in 2026: Where Navier-Stokes Stands

On 7 October 2026 the Clay Mathematics Institute (CMI) still lists only the Poincaré conjecture as solved among its seven Millennium Prize Problems, with Navier-Stokes marked active and the other five marked unsolved. OpenAI said on 8 September 2026 that its system had resolved Navier-Stokes, and on 11 September CMI said it was contemplating the announcement that the problem "has apparently been settled", while calling its own process "deliberately unhurried".

A live prediction on versus asks by when CMI will declare one of the six open problems solved: 31 December 2026, 2027 or 2028. This guide covers what OpenAI and CMI have said, what CMI's rules require, how the prediction settles and what a position can cost you.

The Short Answer

• Six problems are open on CMI's list. The Poincaré conjecture is the only one it lists as solved.
• OpenAI claims Navier-Stokes, but CMI has not declared it solved. Only a declaration from CMI settles the prediction. A proof posted online, however much attention it gets, does not.
• The rules build in a wait. A proposed solution must be published in a qualifying outlet, and at least two years must pass after publication before CMI will consider it.
• The prices at 07:13 on 7 October 2026 (UK time): 2.7p (a 2.7% chance) for the 31 December 2026 answer and 12.5p (a 12.5% chance) for 31 December 2027. A price is the market's estimate between 0p and 100p.
• You can lose the whole amount. A winning contract settles at 100p and a losing one at 0p.

What OpenAI and CMI Have Said About Navier-Stokes

CMI describes the problem as a question about the existence and smoothness of solutions to the equations for fluid flow in three dimensions. The details below come from the pages named, checked on 7 October 2026.

• 8 September 2026, OpenAI: its post says an internal system produced a proof, with a formalisation in the Lean proof assistant, that the equations can develop a singularity in finite time. OpenAI says this resolves the problem and that it does not intend to claim the prize. The post links a paper hosted by OpenAI and a Lean file, and names no journal.
• 11 September 2026, CMI: its announcement says CMI contemplates the announcement that the problem has apparently been settled, that its rules describe how a result is evaluated, that the process is deliberately unhurried and that it will provide updates.
• 7 October 2026, CMI's list: the Millennium Prize Problems page still groups Navier-Stokes under active problems, not solved ones, and does not define the label.

CMI's statement does not say the problem is solved. Its rules say a resolution of Navier-Stokes in either direction goes through the standard evaluation procedure, and whether this one meets them is for CMI to decide.

What CMI Requires Before It Declares a Problem Solved

CMI announced the problems in Paris on 24 May 2000. Its rules, adopted on 26 September 2018 and still the version on its page today, say it does not accept solutions sent directly to it. Before it will consider a proposed solution, three things must hold:

1. Publication. It is published in a qualifying outlet: a refereed mathematics publication of worldwide repute, or one that meets relaxed conditions approved by CMI's board.
2. Time. At least two years have passed since publication.
3. Acceptance. The mathematics community has examined it rigorously and accepted it, as CMI judges.

CMI then decides whether it merits detailed consideration and, if so, convenes an advisory committee of at least three members, at least two of them experts on the problem. The full rules give CMI sole authority, make its decisions final and set no fixed date for the decision. A solution first published in a qualifying journal in October 2026, for example, could not be considered under these rules before October 2028.

The one solved problem shows how long the path can take. Perelman's solution of the Poincaré conjecture appeared in preprints on arXiv.org in 2002 and 2003, and CMI's press release announcing the prize came on 18 March 2010. The other open problems are P vs NP, the Riemann hypothesis, the Hodge conjecture, the Birch and Swinnerton-Dyer conjecture and Yang-Mills and the mass gap.

How This Prediction Settles

Every market on versus names the source that settles it before you trade. Here it is official information from CMI. Each date is a separate answer with its own price, and the cut off for each is 05:59 Central European time on 1 January of the following year, which is 04:59 UK time.

• What counts: CMI gives a Millennium Prize for one of the six open problems, or officially declares one of them solved on its website or in an official communication. A prize is not required.
• What does not count: a proof that is posted or published, however well received, until CMI itself declares the problem solved.

Because the answers are deadlines, more than one can be right: a declaration in June 2027 would make the 2027 and 2028 answers right, and none by the end of 2028 would make none of them right. So the prices do not have to add up to 100p.

Dates and Events That Could Move the Prices

• Any update from CMI. It said on 11 September that it will provide updates and gave no date.
• 31 December 2026. The first deadline, with its cut off at 04:59 UK time on 1 January 2027.

A Worked Example

Say the 31 December 2027 answer trades at 20p. You put 600p into it, which buys 30 contracts. The 2% transaction fee is added on top, 12p, so 612p leaves your balance. If CMI declares a problem solved before the cut off, the 30 contracts settle at 100p each, 3,000p in total. If not, they settle at 0p and the 612p is gone. While the market is open you can sell at the current price: at 10p, the 30 contracts would give you 300p back, a loss but a smaller one than 0p. There is no leverage and no margin call, so the most the position can cost you is the 612p you saw before confirming.

Safer Play is built into the app: deposit limits, loss limits, reality checks, time out and self exclusion, alongside GAMSTOP. The safer play page explains each tool.

Where to Find These Predictions

versus is a prediction market app across politics, finance, sport, AI, crypto and entertainment. Besides the dated prediction, a separate one asks only whether CMI will confirm Navier-Stokes is solved by 31 December 2026. How it works follows one position from opening to settlement, and what market resolution means explains how a result is decided.

versus is licensed by the UK Gambling Commission under account 101143, which you can check on the Commission's public register. Positions settle in ordinary money, not cryptocurrency, and customer money is held separately from company money.

Frequently asked questions

Has the Navier-Stokes problem been solved?

OpenAI says its system resolved it. CMI, whose declaration is what counts, has not declared it solved, and its page still lists the problem as active on 7 October 2026.

How long does CMI take to decide?

Its rules require at least two years after publication in a qualifying outlet before it will consider a proposed solution, then an examination with no fixed end date.

Does an AI-made proof count?

The prediction's rules say it does not matter whether artificial intelligence helped. What matters is a declaration from CMI, which in turn needs publication in a qualifying outlet and acceptance by the mathematics community.

The Bottom Line

This prediction comes down to one event: CMI declaring one of the six open problems solved before each cut off. CMI has said only that Navier-Stokes has apparently been settled, and its rules build in a wait of at least two years. Any position can settle at 0p, so only put in what you are comfortable losing. Prediction markets are entertainment with real money at stake, not a way to make money.

18+ only. Trade responsibly. BeGambleAware.org and GAMSTOP.