9 posts tagged “mathematics”
2025
Basically any resource on a difficult subject—a colleague, Google, a published paper—will be wrong or incomplete in various ways. Usefulness isn’t only a matter of correctness.
For example, suppose a colleague has a question she thinks I might know the answer to. Good news: I have some intuition and say something. Then we realize it doesn’t quite make sense, and go back and forth until we converge on something correct.
Such a conversation is full of BS but crucially we can interrogate it and get something useful out of it in the end. Moreover this kind of back and forth allows us to get to the key point in a way that might be difficult when reading a difficult ~50-page paper.
To be clear o3-mini-high is orders of magnitude less useful for this sort of thing than talking to an expert colleague. But still useful along similar dimensions (and with a much broader knowledge base).
Largest known prime number (via) Discovered on 12th October 2024 by the Great Internet Mersenne Prime Search. The new largest prime number is 2136279841-1 - 41,024,320 digits long.
2024
[… OpenAI’s o1] could work its way to a correct (and well-written) solution if provided a lot of hints and prodding, but did not generate the key conceptual ideas on its own, and did make some non-trivial mistakes. The experience seemed roughly on par with trying to advise a mediocre, but not completely incompetent, graduate student. However, this was an improvement over previous models, whose capability was closer to an actually incompetent graduate student.
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.
2023
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”.
2019
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!
2009
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.”
2004
Python in Mathematics
Python in the Mathematics Curriculum by Kirby Urner is something of a sprawling masterpiece. It really comes in four parts: the first is a history of computer science in education, the second an appraisal of the impact of open source on education and the world at last, the third a dive in to the things that make Python so suitable for enhancing the mathematics curriculum and the fourth a discussion of how computer science and traditional mathematics are likely to play off against each other in the field of high school education.
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Python for teaching mathematics
Kirby Urner provides some great examples of how Python can be used as an aid to understanding mathematics on the marketing-python mailing list. I particularly liked this demonstration of Pascal’s triangle using Python generators:
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