Imagine you found a 'shortcut' through a city that's technically shorter in miles but requires you to drive through a wormhole that doesn't exist yet. That's the OpenAI FFT result: asymptotically faster on paper, practically slower than the 1965 algorithm by a factor of 10^99 at any input size that fits in the observable universe. The standard Fast Fourier Transform, devised by Cooley and Tukey in 1965, computes a length-n Fourier transform in fewer than 5n log₂(n) arithmetic operations — down from the naive n² approach. For n = 1,000,000, that's a 10,000-fold speedup. The question since then has been whether you can shave down that log factor. OpenAI's paper from their recent mathematics dump claims a result where the log(n) term is asymptotically smaller than in standard FFT. The argmin blog post, written by a signal processing expert, runs the numbers and finds the claim is technically true and practically meaningless. The estimated constant hidden inside the big-O notation is approximately 10^100 when n = 10^12. At n = 10^100, the Cooley-Tukey algorithm would still be 10^99 times faster. The algorithm only overtakes the classic FFT at input sizes so large the author can barely express the number. This is what Richard Lipton and Ken Regan call a 'galactic algorithm' — one whose theoretical advantage kicks in at scales that have no physical meaning. The deeper problem is the computational model. The algorithm assumes exact complex arithmetic: storing and multiplying complex numbers at arbitrary precision in a single operation. The numbers involved grow superpolynomially with n, meaning actual memory requirements would be effectively exponential if implemented on real hardware. We do not have computers that can do this. Jacques Morgenstern proved in 1973 that you can't beat ½n log(n) if complex coefficients have bounded magnitude. Nir Ailon later showed you can't beat n log(n) without severe numerical instabilities. The OpenAI result sidesteps both barriers by assuming a model of computation that doesn't correspond to any buildable machine. The blog post's author — writing on argmin, an applied math and optimization blog — didn't read the full paper. They used ChatGPT to extract salient facts, noting with acid humor that 'no one at OpenAI read this paper either.' The critique extends beyond this single result to the culture of theoretical computer science, which the author argues 'actively discourages running algorithms on a computer' and rewards asymptotic results regardless of practical realizability. The matrix multiplication result from the same dump (O(n^2.25) operations) gets the same treatment: the constant is not even estimable. The structural critique is sharp: big-O notation, designed to simplify algorithmic accounting, has become a vehicle for logical laziness. An O(n) algorithm could require 10^80 × n operations and still be called 'linear time.' When the hidden constants and required input sizes both exceed physical reality, the 'faster' label is an artifact of formalism, not an advance in computation. The author argues these results would still have been published at top theory venues (STOC, FOCS) and won awards — which indicts the incentive structure, not the mathematics. The piece concludes that AI is 'really good at automating our worst tendencies' — exploiting the gap between what a field rewards on paper and what matters in practice. The OpenAI math dump becomes less a story about breakthroughs and more a stress test revealing where theoretical CS has become untethered from its nominal subject.
