Simon Willison’s Weblog


4 items tagged “mathematics”


An animated introduction to Fourier Series (via) Outstanding essay and collection of animated explanations (created using p5.js) by Andrei Ciobanu explaining Fourier transforms, starting with circles, pi, radians and building up from there.

I found Fourier stuff only really clicked for me when it was accompanied by clear animated visuals, and these are a beautiful example of those done really well. # 5th June 2024, 3:43 pm


Google DeepMind used a large language model to solve an unsolvable math problem. I’d been wondering how long it would be before we saw this happen: a genuine new scientific discovery found with the aid of a Large Language Model.

DeepMind found a solution to the previously open “cap set” problem using Codey, a fine-tuned variant of PaLM 2 specializing in code. They used it to generate Python code and found a solution after “a couple of million suggestions and a few dozen repetitions of the overall process”. # 16th December 2023, 1:37 am


An Interactive Introduction to Fourier Transforms (via) I love interactive exploitable explanations and this is the best I’ve seen in a while: Jez Swanson breaks down exactly what a Fourier transform does, first by letting you interactively draw and deconstruct wave patterns and then by showing Epicycles andcexplsining JPEG compression. All with not a formula in sight! # 12th January 2019, 2:55 am


Mobius Sliced Linked Bagel. “It is much more fun to put cream cheese on these bagels than on an ordinary bagel. In additional to the intellectual stimulation, you get more cream cheese, because there is slightly more surface area.” # 9th December 2009, 8:03 am