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Unverified50% confidenceFactExact time

In 1984, Spencer, Szemerédi, and Trotter proved the upper bound U(N) ≤ O(N^(4/3)) for the unit distance problem.

1

Sources

50%

Confidence

Medium-term (~90 days)

Relevance

7/2/2026

First Seen

Valid until: 9/30/2026

Sources

OpenAI Cracks Erdős Unit Distance Conjecture: AI Independently Disproves 80-Year-Old Math Problem for the First Time

bilibiliAI技术投降派6/6/2026

Related Claims

Unverified1984年Spencer、Szemerédi和Trotter证明了上界结果U(N) ≤ O(N^(4/3))，即N个点中单位距离点对数不超过N的4/3次方的常数倍85% similar Unverified2010年Larry Guth和Nets Katz利用多项式方法解决了Erdős距离问题，证明n个点至少确定Ω(n/log n)个不同距离59% similar UnverifiedFrostman引理（1935年）断言：如果紧集的s维Hausdorff测度为正，则该集合上存在非零正则Borel测度μ满足μ(B(x,r)) ≤ C·r^s56% similar Unverified陶哲轩与本·格林合作证明了'素数中存在任意长的等差数列'的格林-陶定理56% similar UnverifiedDriscoll-Healy采样定理(1994)指出，对于带宽为B的球面函数，只需在球面上等间距采样2B×2B=4B²个点即可精确重构所有球谐系数56% similar

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