OpenAI's internal model disproves Unit Distance Conjecture…
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OpenAI's internal model disproves Unit Distance Conjecture of Erdos
**Paper by prominent mathematicians (each share their thoughts in separate sections; an interesting read):** https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-remarks.pdf
**Here's the blog post by OpenAI:** https://openai.com/index/model-disproves-discrete-geometry-conjecture/
**The problem:** Given n points in the plane, what is the maximum possible number of pairs of points at distance exactly 1?
Erdos famously conjectured that the answer should be n\^{1 + o(1)} (essentially linear in n). OpenAI's model disproves this by constructing a counterexample that polynomially improves Erdos' bound to n\^{1 + 𝛿} for a universal constant 𝛿 > 0.
#science
**Paper by prominent mathematicians (each share their thoughts in separate sections; an interesting read):** https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-remarks.pdf
**Here's the blog post by OpenAI:** https://openai.com/index/model-disproves-discrete-geometry-conjecture/
**The problem:** Given n points in the plane, what is the maximum possible number of pairs of points at distance exactly 1?
Erdos famously conjectured that the answer should be n\^{1 + o(1)} (essentially linear in n). OpenAI's model disproves this by constructing a counterexample that polynomially improves Erdos' bound to n\^{1 + 𝛿} for a universal constant 𝛿 > 0.
#science
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