OpenAI Model’s Proof of Erdős Unit Distance Problem
This proof is an important milestone for the math and AI communities. It marks the first time that a prominent open problem, central to a subfield of mathematics, has been solved autonomously by AI. It also demonstrates the depth of reasoning these systems now support.
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The proof is available here. The companion paper by leading external mathematicians is available here. You can find an abridged version of the model’s chain of thought here .
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Countdown until this amazing capability is primarily used to scam and surveil people
Countdown until this amazing achievement is revealed to be not as amazing, irreproducible or mostly done by a human.
"Countdown until this amazing capability is primarily used to scam and surveil people"
No need for a countdown, that's already the case.
"Countdown until this amazing achievement is revealed to be not as amazing, irreproducible or mostly done by a human."
Doubtful, unless they're blatantly lying:
"This problem was solved in a completely automated fashion. Our internal model was given an AI-written statement of the problem, and its output was sent to an AI grading pipeline, which indicated high confidence that the solution was correct. It was only after this point that internal human researchers and mathematicians began to examine the solution carefully. After preliminary AI-assisted verification and rewriting, a draft was sent to external mathematicians, including several number theory experts, who confirmed the proof’s correctness (and have already simplified and strengthened the argument). The present manuscript is a human-edited exposition of the autonomously produced solution, with references, reorganized proofs, and additional explanatory material added afterward."
I don't think there's any dissembling here. LLMs are just getting good at these types of mathematical reasoning chains.
