The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?
What it is
Reducible's visual walkthrough of the Fast Fourier Transform, motivated by polynomial multiplication. It shows how the FFT's key ideas can be discovered by asking the right questions.
Why Hacker News recommends it
HN repeatedly calls it a fantastic explanation that made FFT click, with some rewatching it periodically.
- 7 people recommended it
- 8 different months
- 5 strong recommendations
- first 2021, last 2026
What HN commenters said
“I truly enjoy this guy’s videos”
withinboredom, 2021-11 · Strong recommendation · in “Ask HN: Most interesting, mildly impractical, well-written books on software?”
“An excellent and very enjoyable video on the FFT applied to the polynomial multiplication is”
FFT applied to polynomial multiplication
squaredot, 2022-12 · Strong recommendation · in “Understanding Convolutions in Probability: A Mad-Science Perspective”
“That video did the same for me.”
Made FFT concepts click
kippinitreal, 2023-01 · Strong recommendation · in “Ask HN: Concepts that clicked only years after you first encountered them?”
“It derives the FFT algorithm from polynomial multiplication and it’s fantastic . I rewatch it every 6 months or so.”
Derives FFT from polynomial multiplication
tverbeure, 2024-07 · Strong recommendation · in “Convolutions, Fast Fourier Transform and polynomials (2022)”
“the video focuses specifically on the FFT algorithm, not on Fourier transforms in general.”
FFT explainer in 3blue1brown style, focused on the algorithm
jstx1, 2021-10 · Recommendation · in “A gentle introduction to the FFT (2002)”
“This video covers it well”
Covers FFT for polynomial interpolation and multiplication
foooobaba, 2023-02 · Recommendation · in “Polynomial Interpolation”
“I would recommend the youtube video [1] by Reducible for an intuition on how FFT works.”
Intuition for how FFT works in 30 minutes
medbar, 2026-04 · Recommendation · in “Understanding the FFT Algorithm (2013)”
Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.
Topics: fft, polynomial multiplication, algorithms, convolution, signal processing
Also recommended by the same people
commentaryThe Marvel Symphonic UniverseEvery Frame a Painting · 6 HN recommenders · 2017–2026
explainerCan YOU Fix Climate Change?Kurzgesagt – In a Nutshell · 10 HN recommenders · 2021–2026
explainerBut what is the Riemann zeta function? Visualizing analytic continuation3Blue1Brown · 6 HN recommenders · 2017–2023
explainerBut how does bitcoin actually work?3Blue1Brown · 15 HN recommenders · 2017–2024
explainerDarts in Higher Dimensions (with 3blue1brown) - NumberphileNumberphile · 1 HN recommender · 2021–2023
talkSaving Voyager 1! - Bruce Waggoner at !!Con 2024!!Con · 4 HN recommenders · 2024–2026
talkHC2023-K2: Hardware for Deep Learninghotchipsvideos · 2 HN recommenders · 2023–2025
explainerThe Most Underrated AlgorithmVeritasium · 5 HN recommenders · 2022–2024