Will all Millennium prize problems be solved (or proved unsolvable) by 2040?
💡 What the odds say
The market puts this at about a 38% chance — less likely than not.
No money — just record your call and see if you were right. Yes is at 38% right now.
The market sees a 38% chance of solving all seven Millennium Prize problems by 2040, driven by AI's rapid progress in theorem proving but tempered by the extreme difficulty of problems like the Riemann Hypothesis and the track record of only one being solved in 25 years.
📊 Base rate: Of the seven Millennium Prize problems posed in 2000, only one (the Poincaré conjecture) has been solved as of 2026, giving a historical solution rate of about 14% over 26 years.
What's driving it
- • AI's growing role in mathematics, highlighted by IEEE Spectrum's June 2026 article on what it means to be a mathematician when AI does the math, suggests automated theorem proving could accelerate breakthroughs (IEEE Spectrum, Jun 25).
- • The Riemann Hypothesis remains a central hurdle, with a November 2025 article calling it the 'most difficult math mystery,' reinforcing skepticism that all problems will be solved (The Spokesman-Review, Nov 24).
- • A September 2025 report of a Chinese doctor solving a century-old math problem and Google AI potentially winning a Millennium Prize indicates concrete progress, boosting the Yes case (36 Kr, Sep 18).
- • The story of Grigori Perelman, who solved the Poincaré conjecture and rejected the prize, serves as a reminder that even solved problems may not be recognized if the solver declines, complicating the 'proved' criterion (The Times of India, May 15).
The case for YES
- • AI systems like those from Harmonic (backed by Sequoia Capital) are increasingly capable of generating and verifying novel proofs, potentially tackling multiple problems in parallel (Sequoia Capital, Oct 26).
- • The 2025 report of a Chinese doctor solving a century-old problem suggests that individual human breakthroughs, combined with AI assistance, could chip away at the list faster than expected (36 Kr, Sep 18).
- • Live Science's December 2025 coverage of AI solving 'impossible' math problems indicates that the pace of discovery is accelerating, making a 14-year window plausible (Live Science, Dec 19).
The case for NO
- • The Riemann Hypothesis, described as the 'most difficult math mystery,' has resisted all attempts for over 160 years, and no AI breakthrough has yet addressed it directly (The Spokesman-Review, Nov 24).
- • Only one of seven problems has been solved in 26 years, and the remaining six include notoriously hard problems like the Navier-Stokes existence and smoothness and the Hodge conjecture, with no clear path to resolution.
- • Even if AI proves some problems, the requirement that solutions be 'proved unsolvable' for some problems (like the Birch and Swinnerton-Dyer conjecture) adds a separate, difficult task that may not be achievable by 2040.
What to watch
- • Any announcement from the Clay Mathematics Institute of a new solution or a formal proof submission for a specific problem would sharply increase Yes odds.
- • A major AI conference (e.g., NeurIPS 2026 in December) featuring a paper that claims a proof or disproof of a Millennium problem would move odds significantly toward Yes.
- • A prominent mathematician publicly declaring the Riemann Hypothesis unsolvable or providing a rigorous proof of its undecidability would push odds toward No, as it would set a precedent for 'proved unsolvable'.
AI-generated · grounded in recent news + odds · informational only, not advice. Verify on the source platform.
Data from Manifold’s public API, for informational purposes only. PredictPal is not affiliated with any platform and does not facilitate trading.
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How it resolves
Resolved by whoever created the market, at their discretion per the question's description. It's play-money (Mana) and not tied to an official source — treat it as a community forecast.
ⓘ A market settles under its own written rules, which can lag what looks decided in the news — so the price may not move to 100% the moment an outcome seems obvious.
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