Resolution criteria

This market will resolve to YES if all seven Millennium Prize Problems are officially resolved before the Collatz Conjecture is officially resolved.

This market will resolve to NO if the Collatz Conjecture is officially resolved before all seven Millennium Prize Problems are officially resolved.

Definitions and Rules:

• Millennium Prize Problems: The seven problems designated by the Clay Mathematics Institute in 2000:

  1. Poincaré conjecture (officially resolved)

  2. Birch and Swinnerton-Dyer conjecture

  3. Hodge conjecture

  4. Navier–Stokes existence and smoothness

  5. P versus NP problem

  6. Riemann hypothesis

  7. Yang–Mills existence and mass gap

• Collatz Conjecture: The mathematical conjecture concerning the behavior of the sequence $3n+1$.

• "Officially resolved": A problem is considered resolved if a proof, disproof, or proof of undecidability (e.g., independence from ZFC) is published in a reputable peer-reviewed mathematical journal and achieves a broad consensus of acceptance within the global mathematical community (such as acknowledgement by the Clay Mathematics Institute, the International Mathematical Union, or major academic bodies). Alternatively, a Lean or otherwise computer verified proof will count as long as the mathematical community accepts it.

• If the last remaining Millennium Prize Problem and the Collatz Conjecture are resolved within the same calendar month or the order of resolution is highly ambiguous, the creator will resolve the market based on the publication date of the earliest accepted peer-reviewed paper or verified preprint of the valid proofs.

Background

The Clay Mathematics Institute established the seven Millennium Prize Problems in 2000, offering a $1 million prize for each solution. To date, the Poincaré conjecture remains the only officially solved problem (by Grigori Perelman). In September 2026, OpenAI published a proposed proof for the Navier–Stokes existence and smoothness problem. However, like all proposed mathematical breakthroughs, it remains subject to extensive community verification and formal peer review.

The Collatz Conjecture, while not a Millennium Prize Problem, is one of the most famous and deceptively simple unsolved problems in number theory. This market asks whether mathematicians will completely wrap up the Millennium list before finally cracking the Collatz Conjecture.

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