OpenAI's Problem #130 breaks n log n: exact DFT now O(n(log n)^0.99925)
generativist · x · 2026-10-10
An update to OpenAI's community project Problem #130 reports an exact discrete Fourier transform algorithm below n log n: T(n) = O(n(log n)^(1−δ)) with δ = 0.0007547360, a 10.34x improvement over the previously announced δ = 7.3×10⁻⁵.
- The stronger Fourier bound comes from Jacob Sussman's five-stage framework and Chafik Boukhalfa's improved construction, building on work by the OpenAI and open community contributors.
- As one commenter quipped, it's a "real speedup": the asymptotic gain only beats the standard O(n log n) algorithm by 1% at n as small as 10^600000 — theoretical significance far beyond practical use.
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