Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
Reddit user xilefakamot created this in 2020 — a “topologist’s map of the world.” It depicts international borders and nothing else — the shapes, sizes, and distances between countries are forsaken in order to present the pattern of their borders as efficiently as possible. “No calculations per se – I sketched out a…
An interdisciplinary team of mathematicians, engineers, physicists, and medical scientists have uncovered an unexpected link between pure mathematics and genetics.
This post illustrates a key lemma that is used in proving the fundamental theorem of Galois theory (FTGT). Note that FTGT is not covered in this post. The focus of this post is on understanding and proving this lemma only. Here is the lemma from the book Galois Theory , 5th ed. by Stewart (2023):
I recently went on a nice long SCUBA diving trip with my wife and daughters. Lots of diving implies lots of showers, and lots of showers means lots of shower-thoughts! [1] An especially interesting one I had turned into a nice way to visualize some aspects of the Collatz Conjecture.
In his book Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, G. H. Hardy tells this famous story: He could remember the idiosyncracies of numbers in an almost uncanny way. It …
The geometry of random walks in high dimensions provides the power behind deep learning and may be the secret to intelligence.
I first participated in Advent of Code (AoC) in 2017. My co-workers at Formlabs introduced it to me. This year (2018), quite a lot of Formlabs folks are taking part and we have a nice private leaderboard going. I'm having a lot of fun with it. I've been staying up until midnight to work on the problems as soon as…
The eigenvectors of a circulant matrix do not depend on the matrix itself, only on the size, and the eigenvectors are columns of the FFT matrix.
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Watabou’s Cave Generator is one in a series of RPG-ready map generators that Watabou has created over the years. All his work oozes style, but the cave generator was always the one I found mo…
Educators can show in secondary school maths that AI systems don’t think, making maths more interesting while teaching core concepts of AI.
[ An updated treatment of some of this material appears in Chapter 2 of the Energy and Human Ambitions on a Finite Planet (free) textbook, also mirrors a 2022 article in Nature Physics . . ]
Are you kidding? Edward Barbeau is now a professor emeritus of mathematics at the University of Toronto. Over the years he has been working to increase the interest in mathematics in general, and e…
There is hardly ever a good reason to invert a matrix. What do you do if you need to solve Ax = b where A is an n x n matrix? Isn't the solution A−1 b? Yes, theoretically. But that doesn't mean you need to actually find A−1. Solving the equation Ax = b is
Matt Parker, employing the enviably pithy prose typical of a content creator forged on the unforgiving fires of social media, asked the simple question back in 2018: > How thick is a three-sided coin? Translated into mathematician-ese, this means > What aspect ratio of a flipped coin leads to the chance of landing on…
Shamir's Secret Sharing Scheme
If you’re familiar with nearly any mainstream programming language, and I asked you to draw a diagram of an array, the array indices, and the array elements, odds are good you’d produce a diagram something like this: In this post, I want to persuade you to replace that image, or, at least, to augment it with an…
When I first learned about Diffie-Hellman and especially elliptic curve Diffie-Hellman, I had one rather obvious question: Why elliptic curves? Why use this strange group that seems rather arbitrar…
Implementing strict three point perspective is ridiculous. You’ll never need it. Let’s do it anyway.
The Latest News from Research at Kudelski Security
Quanta Books is delighted to announce two new upcoming books by mathematician Terence Tao and theoretical physicist David Tong. Six Math Essentials will be Tao’s first math book written for a popular…
