MatthewBarnett avatar
Matthew Barnett
closes Jan 2, 2030
Will an AI solve any important mathematical conjecture before January 1st, 2030?
71%
chance

For the purpose of this question, a mathematical conjecture is considered "important" if it appears on the list of unsolved problems maintained by the following sources:

  • The Clay Mathematics Institute (CMI)

  • The Unsolved Problems in Number Theory book by Richard K. Guy

  • The Open Problem Garden (http://garden.irmacs.sfu.ca/)

These sources collectively provide a broad variety of conjectures across different fields of mathematics that are widely acknowledged as significant.

This question will resolve as "Yes" if, before January 1st, 2030, an AI system fully solves any important mathematical conjecture on the combined list of unsolved problems from the mentioned sources, and the solution:

  • Is published in a reputable mathematics journal. For the purpose of this question, a reputable mathematics journal is defined as a journal meeting each of these criteria:

    • Peer Review: The journal must have a well-defined, rigorous, and transparent peer-review process.

    • Indexing: The journal should be indexed in at least one of the following well-known databases: MathSciNet, Web of Science, or Scopus.

    • Impact Factor: The journal must have an impact factor greater than or equal to a threshold of 1.0, as reported by either Clarivate Analytics Journal Citation Reports or Scimago Journal Rank (SJR).

  • Is accompanied by a clear and detailed proof or argument that is deemed valid by the journal's reviewers.

  • Has not been retracted or shown to be incorrect within six months of publication.

  • Is explicitly attributed to an AI system in the published article, with a clear description of the AI's role in deriving the solution.

To determine whether the AI played an essential role in the solution, the following criterion must be met:

The AI must have autonomously discovered the primary breakthrough, insight, or technique that was instrumental in solving the conjecture. This breakthrough, insight or technique must be easily succinctly and accurately summarizable within a combined total of 5000 words and 2000 mathematical symbols, such that if that summary had been handed to a mathematician working in the same area just a few years prior, then that mathematician would likely have been able to solve the full conjecture within a year without the aid of any AI more advanced than what existed in 2015.

To measure this, the published article should:

  • Explicitly identify the AI's discovery of the primary breakthrough, insight, or technique.

  • Explain how this discovery was pivotal in solving the conjecture.

  • Provide evidence that this discovery was a major challenge for human mathematicians to discover, such as citing prior unsuccessful attempts or highlighting the novelty of the AI's approach.

To determine whether the AI's discovery was "pivotal", the following aspects should be examined in the published article:

  • Necessity: The article should explain why the AI's discovery was necessary for the solution, demonstrating that without this discovery, the conjecture would remain unsolved or the proof would be invalid.

  • Novelty: The article should highlight the novelty of the AI's discovery, showing how it differs from previous approaches and why it was instrumental in resolving the conjecture. This can include a comparison to earlier attempts that were unsuccessful or an explanation of the unique aspects of the AI's approach.

  • Impact: The article should discuss the impact of the AI's discovery on the solution process, such as how it led to the development of other essential components of the proof or how it provided a new perspective that enabled the resolution of the conjecture.

The question will resolve as "No" if no AI system fully solves any important mathematical conjecture on the combined list of unsolved problems from the mentioned sources according to the above criteria before January 1st, 2030.

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PatrickDelaney avatar
Patrick Delaney

Tangentially related:

JasonHoelscherObermaier avatar
Jason Hoelscher-Obermaier

published in one of the following major mathematical journals: Annals of Mathematics, Journal of the American Mathematical Society, or Inventiones Mathematicae.

Why the restriction to these journals?

There seem to be a bunch of other journals with similar scimago ranks:

StrayClimb avatar
Reynoldsis predicting YES at 78%

@JasonHoelscherObermaier I have similar questions. If one of those conjectures were solved, and all other criteria meet, how likely would it be to be published on one of that short list of journals?

MatthewBarnett avatar
Matthew Barnett

@StrayClimb OK I intend to re-write this part of the question later today to expand the list of journals. FWIW, this question was written by GPT-4.

MatthewBarnett avatar
Matthew Barnett

@JasonHoelscherObermaier I have now re-written the question to provide a better standard for what journals should count.