Resolution criteria

This market resolves to the entity or organization that is primarily credited with providing the first widely accepted proof resolving the "P versus NP" problem (whether $P = NP$ or $P \neq NP$).

• Verification Standard: A solution will be considered valid if it meets consensus acceptance within the theoretical computer science / mathematics community, signified by:

  • Acceptance and publication in a reputable peer-reviewed mathematics or theoretical computer science journal, and/or

  • Formal recognition by the Clay Mathematics Institute for the Millennium Prize Problem award.

• Answer Options:

  • Human (Independent / Academia): Resolves YES if the proof is authored by an individual or academic research team without an AI system playing the central, generative theorem-proving role, and outside of primary affiliation with the specific corporate frontier labs listed.

  • OpenAI: Resolves YES if an AI model or research team developed by OpenAI is primarily credited with finding or generating the core proof.

  • Anthropic: Resolves YES if an AI model or research team developed by Anthropic is primarily credited with finding or generating the core proof.

  • Google (Gemini or DeepMind): Resolves YES if an AI model or research team developed by Google / Google DeepMind is primarily credited with finding or generating the core proof.

  • Other: If an entity, organization, or corporate lab not listed above generates the accepted proof, the market will resolve to "Other" (or that entity's answer option if added).

• Ambiguity / Collaboration: If an unassisted human uses an AI simply for formatting, typing, or routine search verification, it resolves to the human/academic option. If an autonomous or semi-autonomous AI system produces the key mathematical insights/steps, it resolves to the creator/maintainer of that AI system.

• If no accepted proof is produced before market close, or if multiple answers claim credit simultaneously without consensus, resolution will follow official Clay Mathematics Institute announcements or the creator's discretion based on major community consensus.

Background

The P versus NP problem is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000, carrying a $1,000,000 prize for the first correct proof. It asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.

Most complexity theorists conjecture that $P \neq NP$. Over the decades, dozens of purported proofs have appeared on preprint servers such as arXiv, but all have either been refuted or found to contain fatal gaps. With the rise of automated reasoning, interactive theorem provers (like Lean), and frontier AI systems (e.g., DeepMind's AlphaProof, OpenAI, and Anthropic research), there is an active debate over whether the problem will fall to human mathematicians, frontier AI models, or hybrid collaborations.

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