The latest blog posts to take off on Hacker News. 2,391 posts.
28 . That's the minimum number of AND or OR operators you need in order to write any Boolean function of five variables. Alex Healy and I computed that in April 2010. Until then, I believe no one had ever known that little fact. This post describes how we computed it and how we almost got scooped by Knuth's Volume 4A…
Personal website of David R Hagen, scientific software engineer
There is a well-known puzzle based on the premise of an �infinite� grid of resistors connecting adjacent nodes of a square lattice. A small portion of such a grid is illustrated below.
Introduction In this blog post you are going to read about two things:
Cantor conceived set theory in a sequence of six papers published in the Mathematische Annalen during the five year period 1879–1884. In the fifth of these papers, published in 1883, 1 he stated as a law of thought ( Denkgesetz ) that every set can be well-ordered or, more precisely, that it is always possible to…
For sure easier than solving it in SAT!
Discovering Atari Games in Randomly Generated Data
David Zuckerman The 2025 Gödel Prize has been awarded to Eshan Chattopadhyay and David Zuckerman for their paper Explicit two-source extrac...
I reflect on the Entscheidungsproblem how it relates to Sudoku solvers. It's a little weird. .
Brief discussion on gaussian quadrature and chebyshev-gauss quadrature
Just as I was complaining that we haven't seen many surprising breakthroughs in complexity recently, we get an earthquake of a result to st...
You've most likely heard about gradient noise through the name Perlin noise , which refers to one particular implementation with various CPU optimizations. Because it's an incredible tool for creative work, it's used virtually everywhere: visual effects, video games, procedural mathematical art, etc. While getting it…
Almost 20 years ago, I wrote a textbook in real analysis called “Analysis I”. It was intended to complement the many good available analysis textbooks out there by focusing more on foun…
At the New England Symposium on Graphics , James Tompkin compared graphics researchers to magpies: they're easily distracted by shiny objects and pretty renderings.
While reading through the fantastic book *[The Lost Art of Logarithms](https://www.lostartoflogarithms.com/)* by [Charles Petzold](https://www.charlespetzold.com/) I was nerd-sniped by a [simple method](https://www.lostartoflogarithms.com/chapter04/) of estimating the logarithm of any number base 10. According to the…
At least a familiarity with the lambda calculus, including how it is evaluated. Some base knowledge of programming languages is also assumed.
For Pycon 2025, I created a poster exploring vector embedding models, which you can download at full-size . In this post, I'll translate ...
An explainer for people who don't know computer science and are mildly curious
The story starts in Crosscord, the crossword Discord server. Over 5,000 users strong, the server has emerged as a central hub for the online crossword community, a buzzing, sometimes overwhelming, sometimes delightful town square where total noobs, veteran constructors, and champion solvers alike come together to talk…
Explore Bill Benter’s iconic horse betting strategy, enhanced with modern code and contrasted against three decades of evolving data.
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…
Celebrating a rare dumpster fire in the kingdom of science.
This is a post about multiplying polynomials, convolution sums and the connection between them.
Everything lives on a manifold
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.
Transformer-based large language models are relatively easy to understand. You break language down into a finite set of “tokens” (words or sub-word components…
How to test for leap years (until year 102499) in the proleptic Gregorian calendar with just three 32-bit instructions, with detailed explanation of the bit-level tricks.
Usually I write about solutions to problems I’ve worked out, but I’ve found myself increasingly becoming interesting in where solutions come from. Maybe it’s because I’ve been reading Boorstin’s excellent The Discoverers , which I’d strongly recommend.
Exploring a peculiar bit-twiddling hack at the intersection of 1980s geek sensibilities.
