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The most popular blog posts about math & algorithms on Hacker News. 150 posts.
Bayesianism, the doctrine that it's always rational to represent our beliefs in terms of probabilities, dominates the intellectual world, from decision theory to the philosophy of science. But does it make sense to quantify our beliefs about such ineffable things as scientific theories or the future? And what separates
This post describes the implementation of pysmtgcc. See “GCC Translation Validation” for background information.
In this post we'll work our way towards an algorithm that can compute convex polygon intersections. We'll also explore a method for intersections between axis-aligned rectangles, a function that can determine the intersection of two line segments, as well as a point in polygon test.
Researchers have calculated the quantum computer size necessary to break 256-bit elliptic curve public-key cryptography: Finally, we calculate the number of physical qubits required to break the 256-bit elliptic curve encryption of keys in the Bitcoin network within the small available time frame in which it would…
Milton Friedman’s interest rate fallacy is one of the most mystifying and counterintuitive facts in modern finance.
Binary lambda calculus ( BLC ) is a minimal, pure functional programming language invented by John Tromp in 2004, 1 based on a binary encoding of the untyped lambda calculus in De Bruijn index notation.
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Audio Link With the arrival of summer weather in many parts of the U.S., it’s time to think again about various outdoor activities. Wat...
How does set theory help to understand type assignability and resolution in TypeScript?
This is a guest post, written by Zhangir Azerbayev. Zhangir is an undergraduate at Yale, majoring in computer science and mathematics. He completed this work while visiting Carnegie Mellon’s …
18 x 93 is… hey, look over there!
This post is an unofficial sequel to one of my first blog posts from 2007, which was entitled “Quantum mechanics and Tomb Raider”. One of the oldest and most famous allegories is Plato&…
You sometimes feel the need to make all of your integers positive, without losing any information. That is, you want to map all of your integers from 'signed' integers (e.g., -1, 1, 3, -3) to 'unsigned integers' (e.g., 3,2,6,7). This could be useful if you have a fast function to compress integers that fails to ……
The word "kayak" is a palindrome, but it isn't visually symmetric. The word "bud" is visually symmetric, but not a palindrome.
Description of the film grain synthesis algorithm in AV1. This page provides information on the film grain synthesis algorithm and links for further study
Tetration -- repeated exponentiation a fractional number of times.
Whenever a student wonders why linear algebra, matrices, and vectors are important, the response from teachers usually sounds like this:
Where do you stand in order to minimize the expected distance to walk to catch the first elevator that arrives? Maybe not where you think.
Why does lining up two scales of a slide rule let you multiply numbers?
Graphists, animators, game programmers, font designers, and other graphics professionals and enthusiasts are often working with Bézier curves. They're popular, extensively documented, and used pretty much everywhere. That being said, I find them being explained almost exclusively in 2 or 3 dimensions, which can be a…
Elliptic Curve Cryptography (ECC) has grown to be very popular in public-key cryptographic systems, most popularly used in Bitcoin. ECC is…
Noether's theorem is an amazing result which lets physicists get conserved quantities from symmetries of the laws of nature. Time translation symmetry gives conservation of energy; space translation symmetry gives conservation of momentum; rotation symmetry gives conservation of angular momentum, and so on.
Start with any triangulation of a convex polygon, and then repeatedly choose a random diagonal and flip it, replacing the two triangles it borders with two d...
The ability to quick estimates is still valuable, maybe more valuable than it used to be.
Bill Harris points to this cartoon from Randall Munroe. I think he (Munroe) is really on to something here. Not about Bayes’s theorem but about the sorts of examples that are in textbooks.
[ An updated treatment of this material appears in Chapter 1 of the Energy and Human Ambitions on a Finite Planet (free) textbook , and also appears as part of an article in Nature Physics in 2022.]
When you first read about "torsors", they're bound to seem a bit too darn sophisticated for their own good. Mostly this is because nobody explains them very well. So, I want to convince you that they're actually very simple and natural. I'll do this by giving you three examples from physics:
