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Computing primes with CSS
I’ve been working on a redesign of this site, so doing more CSS, finally internalizing Sass, etc. During my reading, the nth-child pseudo-class caught my eye.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
2402
Gödel's Incompleteness Theorem explained
This theorem is one of the most important proven in the twentieth century. Here are a few brief selections that will help you start to understand it. Gödel’s original paper “On Formally Undecidable Propositions” is available in a modernized translation . It’s also in print from Dover in a nice, inexpensive edition …
2403
Optimizing Your Wife
If a man can expect to meet exactly N eligible women in his life, what strategy should he use to maximize his chances of choosing the very best one? We typically make some idealized assumptions when solving this type of problem, such as assuming that he meets the women in random order of "goodness", that there is an…
2404
The Holy Trinity: Logic, Languages, Categories (2011)
The Christian doctrine of trinitarianism states that there is one God that is manifest in three persons, the Father, the Son, and the Holy Spirit, who together form the Holy Trinity. The doctrine…
2405
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:
2406
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...
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(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.
2410
Which Is Closer: Local Beer or Local Whiskey?
For which fraction of the US is the nearest brewery further away than the nearest distillery? Analysis and visualization done with Wolfram Language.
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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{{{<}…
2413
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…
2414
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…
2415
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…
2416
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.
2417
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…
2418
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 …
2419
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 …
2420
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...
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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…
2423
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 …
2424
Why are mathematicians so bad at arithmetic? (2017)
18 x 93 is… hey, look over there!
2425
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.
2426
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.
2427
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…
2428
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...
2429
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…
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