2011
Maybe the spaghetti code conjecture is false
The Spaghetti Code Conjecture says that Busy Beaver programs ought to be, in some sense, as complicated as possible. Scott Aaronson puts it this way:
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,393 posts.
2012
If Scheme's numbers were like Scheme
Scheme's numbers are not like the rest of its library. They're older, and they're mostly borrowed from other languages (Maclisp and Common L...
2013
2014
2015
(Post-Quantum) Cryptographic Right Answers
In the tradition started by Colin Percival and Thomas Ptacek, a set of “Cryptographic Right Answers” updated for the accelerated post-quantum transition timeline.
2016
2017
The lattice of sets of natural numbers is rich (2021)
$\newcommand\of{\subseteq}\newcommand\N{\mathbb{N}}\newcommand\R{\mathbb{R}}\def\<#1>{\left\langle#1\right\rangle}\newcommand\Z{\mathbb{Z}}\newcommand\Q{\mathbb{Q}}\newcommand\ltomega{{{<}…
2018
Squares in Squares
The following pictures show $n$ unit squares packed inside the smallest known square (of side length $s$). If a pictured packing has multiple numbers in its label above, the picture represents the largest; each smaller is represented by removing any square. For the $n ≤ 324$ not pictured, the trivial packing (with no…
2019
Toward an exploratory medium for mathematics
The world's oldest complete piece of surviving music is the 3,400-year-old Hurrian cult hymn . The hymn was found inscribed on clay tablets excavated from the ancient city of Ugarit, in modern-day Syria. Sometime after the hymn was composed, the idea of using notation to record music was lost. Writing two millennia…
2020
Perfecting anti-aliasing on signed distance functions
Doing anti-aliasing on SDF is not as straightforward as it seems. Most of the time, we see people use a smoothstep with hardcoded constants, sometimes with screen space information, sometimes cryptic or convoluted formulas. Even if SDFs have the perfect mathematical properties needed for a clean anti-aliasing, the…
2021
Latitude doesn’t exactly mean what I thought
There are two kinds of latitude: geocentric and astronomical. On a perfect sphere, they're the same, but on an oblate spheroid like Earth they're different.
2022
Formalising modern research mathematics in real time
(This is a guest post by Bhavik Mehta) On March 16, 2023, a paper by Campos, Griffiths, Morris, and Sahasrabudhe appeared on the arXiv, announcing an exponential improvement to the upper bound on R…
2023
The future of interactive theorem proving?
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 …
2024
Quaternion Differentiation (2012)
I wanted to point someone to a short explanation of this today and noticed, with some surprise, that I couldn’t find something concise within 5 minutes of googling. So it seems worth writing …
2025
Using Python and heat maps to determine the best place to aim on a dart board
Over break I went out with a buddy of mine and played some darts. This got me to thinking, where exactly should someone aim in order t...
2026
2027
Curve fitting A: Linear Least Squares
The graph on the left shows a third example, taken from analytical chemistry: a straight-line calibration data set where X = concentration and Y = instrument reading (Y = a + b X). Click to download that data . The blue dots are the data points. They don't all fall in a perfect straight line because of random noise…
2028
The Axiom of Choice Is Wrong (2007)
When discussing the validity of the Axiom of Choice, the most common argument for not taking it as gospel is the Banach-Tarski paradox. Yet, this never particularly bothered me. The argument …
2029
Why are mathematicians so bad at arithmetic? (2017)
18 x 93 is… hey, look over there!
2030
Truth is not a direction: a Tarski attack on LLM probes
Abel Jansma is a scientist studying emergence, higher-order interactions, information theory, and complex systems across biology and artificial intelligence.
2031
How to Think about Correlation?
I am an economist at the Federal Trade Commission with a very basic statistics question, one that I have put to several fairly high-powered econometricians, and to which no one has had a satisfying answer.
2032
Inverting the Xorshift128 random number generator
CVE-2025-7783 is a very recent vulnerability affecting a lot of applications in the Node.js ecosystem including those which use axios or the deprecated request library. In all honesty, this vulnera…
2033
What objective is reasoning solving?
Reasoning as pathfinding in token space.
2034
The new Gödel Prize winner tastes great and is less filling
David Zuckerman The 2025 Gödel Prize has been awarded to Eshan Chattopadhyay and David Zuckerman for their paper Explicit two-source extrac...
2035
Losing the Nobel Prize
There’s a fascinating new book just now appearing in book stores, Losing the Nobel Prize, by astronomer Brian Keating. An excerpt from the book is available at Nautilus, with the title How My…
2036
2037
How Useful Is Tufte for Making Maps? (2007)
Edward Tufte’s The Visual Display of Quantitative Information (1998, 2nd edition 2001) is a classic book, arguably his best, and certainly a key text in the field of information graphics (whi…
2038
What is static program analysis?
The halting problem asks whether the execution of a specific program for a given input will terminate.
2039
Who Expected That? Extreme close-ups create a Klein Bottle.
Suppose you go around taking extremely close-up black-and-white pictures of randomly chosen natural and unnatural objects (rocks, trees, streams, buildings, etc.). What do they look like? Well, eac…
2040
Solving a “Layton Puzzle” with Prolog
I have a lot in the works for the this month's Logic for Programmers release. Among other things, I'm completely rewriting the chapter on Logic Programming...