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OpenAI Aftermath is a guide to mathematical research published by OpenAI and to publicly available follow-up work by others: extensions, applications, formal verifications, corrections and critiques.

How entries are written

• Each result page summarizes the published claim and cites its public source: the paper, the repository commit or the preprint version.
• Follow-up work is listed with its relation to the original result (extension, use, verification, correction or critique), its public date and its public status.
• The publication of a paper, code or a formal proof is reported as such. It is not presented as independent verification.

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• All result pages
• Number theory:
  • Irrationality of Catalan's constant
  • The irrationality exponent of π is 2
  • Modularity of elliptic curves over imaginary quadratic fields
  • The quasi-Riemann hypothesis
• Convex geometry:
  • The Mahler conjectures
• Algebraic complexity:
  • Matrix multiplication with exponent at most 9/4
• Discrete geometry:
  • The Euclidean plane is not five-colorable

Sources

• OpenAI mathematics collection: github.com/openai/math