OpenAI Publishes Proof Refuting Erdős's Conjecture

OpenAI's internal general-purpose reasoning model has generated a proof that refutes the planar unit distance conjecture proposed by Paul Erdős. This model announced a construction related to the conjecture raised by Erdős in 1946 on May 20. The planar unit distance problem is a combinatorial geometry question that asks how many pairs of points can be placed on a plane such that each pair is exactly one unit apart. The published proof demonstrated that for any positive δ, it is possible to create at least n^(1+δ) unit distance pairs for infinitely many n. Professor Will Sawin from Princeton University proved that δ could be set to 0.014 during the subsequent refinement process. External mathematicians, including Noam Alon and Thomas Bloom, reviewed the counterexamples generated by the model and published a companion paper. Mathematician Gowers described this result as a 'milestone in AI mathematics.' OpenAI submitted proof attempts for ten problems on February 20, determining a high likelihood of correct answers for problems 4, 5, 6, 9, and 10. However, this achievement is unrelated to blockchain or cryptocurrency, and there is no evidence that AI has attacked the signature systems of Bitcoin or Ethereum. The cryptography community is currently working on transitions to address the threats posed by quantum computers, and NIST is expected to approve three post-quantum cryptography standards on August 13, 2024.

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