The latest blog posts to take off on Hacker News. 2,851 posts.
To be fair, nobody asks me this exact question. But people have regularly asked why Isabelle dispenses with proof objects. The two questions are essentially the same, because proof objects are intrinsic to all the usual type theories. They are also completely unnecessary and a huge waste of space. As described in an…
In which I explore the biggest barrier in the busy beaver game. What is Antihydra, what is the Collatz conjecture, how are they connected, and what makes them so daunting?
The ratio 987654321 / 123456789 is very nearly 8. What about the analogous ratio in other bases?
Deriving the basic mathematical properties of the Smith chart from electrical engineering
Lambda calculus is for wimps. Real programmers use combinatory logic.
This post covers the same material as my !!Con 2024 talk , for which the slides are here .
I read a good post by one of the authors of the Isabelle theorem prover, that got me thinking. The author, Lawrence Paulson, observed that most math proofs are trivial, but writing them (preferably with a proof assistant) is a worthwhile activity, for reasons similar to safety checklists - “Not every obvious statement…
I’m a great believer in low-tech math. I don’t like to rely on things a computer tells me; what if there’s a bug in the code? I prefer trusting things that I can check for myself. At the same…
Bézier curves are a core building block of text and 2D shapes rendering. There are several approaches to rendering them, but one especially challenging problem, both mathematically and technically, is computing the distance to a Bézier curve. For quadratic curves (one control point), this is fairly accessible, but for…
This article is about a new kind of simple computational rule ("LACE rules" running on LACE, the Link Automata Computing Engine platform) which, when applied locally on a grid of cells, demonstrates fascinating emergent "artificial life" behavior.
On June 30, 2025, Mark Brittenham and Susan Hermiller uploaded a preprint to the arXiv called “Unknotting number is not additive under connected sum” (and an updated version on Septembe…
|| Paper | Code ||
We’re excited to announce Flummoxagon, a new geometric puzzle game that might just leave you flummoxed. Imagine a mash-up of Pentominoes and Sudoku. Your goal is to fit all the pieces into the hexa…
Chapter 1: Row vs column picture
I have a side project to find the longest line of sight on the planet 1 using a novel Total Viewshed algorithm . At a resolution of 3 arc-seconds (~92m x 92m), the planet contains around 4.5 billion elevation samples 2 . Now obviously we don’t need to calculate the visibility between literally every single one of…
In computer science, we often compare the efficiency of algorithms by describing their runtime as a function of the size of the input. Sorting is O(n * log(n)), meaning that sorting a list of N items takes an amount of time proportional to the number of items multiplied by its logarithm. Matrix multiplication is…
When you resize, rotate, or in any way transform an image; or more generally when you resample some discrete signal, the software you are using must _interpolate_ between the discrete points to produce a result. Linear and cubic interpolation are easy to explain, but Lánczos interpolation, one of the most popular…
This is the companion website for the paper Understanding Optimization in Deep Learning with Central Flows , published at ICLR 2025.
I didn’t invent categories to study functors; I invented them to study natural transformations. — Saunders Mac Lane
How I overcame copying and modifying my own diff library from project to project by diving too deep into diff algorithms and coming out at the other end with new diff library in my hand.
Contribution by Philip Ham: attractor.basic and Python implementation by Johan Bichel Lindegaard.
What's the meaning of "numbers" and "arithmetic operations"? We consult Georg Cantor's turtles and look at Giuseppe Peano's code.
The number of characters was 464 characters at first, but thanks to the community it got reduced further, and the article updated accordingly.
Posts and writings by Julian Schrittwieser
A geometric framework for co-designing neural net optimizers with manifold constraints.
Quarto Academic Website Template adapted by Dr. Gang He
Stephen Wolfram explains the rich ruliology of lambdas, made particularly significant by their connection to practical computing. Covers basic computations to undecidability to multiway graphs and evaluation strategies.
Exploring the world of constraint solvers with very simple examples.
