The article critiques OpenAI's recent claim of a faster Fourier transform, arguing it is not a genuine breakthrough but rather a misuse of big-O notation and formalism detached from practical computation. It explains that the Fast Fourier Transform (FFT), developed by Cooley and Tukey in 1965, remains a cornerstone of digital signal processing, enabling efficient frequency analysis through a recursive divide-and-conquer approach that reduces complexity from O(n²) to O(n log n). The author emphasizes that while theoretical improvements to the FFT's prefactor are sought, OpenAI's proposed 'improvement' fails under scrutiny, revealing instead a breakdown in mathematical rigor where notation is manipulated to produce misleading results.
The piece warns that such work reflects a broader trend in AI-generated mathematics, where outputs are fed back into models without validation, creating an echo chamber of unsubstantiated claims. Ultimately, the author concludes that no real speedup was found — only the rot of formalism unmoored from meaning, where the appearance of progress masks a failure to properly define computational problems in natural language.
Source: Hacker News · Summarized by HeadlinesBriefing