Unverified50% confidenceOpinionExact time
For a long time, n log n has been regarded by many as a kind of natural lower bound on the complexity of integer multiplication, closely tied to the information-theoretic intuition of the FFT.
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10/13/2026
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UnverifiedThe academic community conjectures that the optimal complexity lower bound for integer multiplication is Ω(n log n), but this has not been rigorously proved to date and remains an empirical conjecture.78% similarUnverifiedNTT (Number Theoretic Transform) can reduce the complexity of polynomial multiplication from O(n²) to O(n log n).73% similarUnverifiedQuicksort has an average time complexity of n log n and degrades to O(n²) in the worst case.73% similarUnverifiedThe Schönhage–Strassen algorithm leverages the Fast Fourier Transform (FFT) to reduce integer multiplication complexity to O(n log n log log n).69% similarUnverifiedSimply changing the definitional order of the error metric causes the number of rounds required for sampling to collapse from (log n)^2 to the log ln n scale, constituting a large asymptotic separation.67% similar
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