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Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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A new rare high-rank elliptic curve, and an orchard of Diophantine equations
I got an email the other day from mathematician Bogdan Grechuk, whose book Polynomial Diophantine Equations: A Systematic Approach ( was recently released. This is to my mind a rather remarkable bo…
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Making the Monty Hall problem weirder but obvious
It’s this simple: Do you want what’s behind one door or the other nine?
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Gödel and the unreality of time
In 1949, in a festschrift devoted to Einstein , Kurt Gödel published a very short but profound paper titled “A Remark About the Relati...
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Sub-pixel distance transform
High quality font rendering for WebGPU
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Wounded QR Codes
How do QR codes work? How much is it possible to distort one and still have it readable?
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The art of solving problems with Monte Carlo simulations
Using the power of randomness to answer scientific questions.
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Fusion Foolery
Great. The fusion hype is bad enough already. Now its resurgence is going to interrupt the series of posts I’m in the middle of publishing in order for this post to be “timely.”
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There's more to mathematics than rigour and proofs (2007)
The history of every major galactic civilization tends to pass through three distinct and recognizable phases, those of Survival, Inquiry and Sophistication, otherwise known as the How, Why, and Wh…
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A trick to eliminate 2π (sometimes)
As a physicist, I’ve learned that the presence of 2 π 2\pi 2 π [▼] [ Or rather τ \tau τ , as it should actually be called . ] in a formula usually spells trouble. It’s kind of annoying to write by hand, easy to forget, and it’s dimensionless, so you can’t easily check if you forgot to divide or multiply by it…
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Can a Rubik's Cube be brute-forced?
a personal blog
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My favorite prime number generator
Many years ago I've re-posted a Stack Overflow answer with Python code for a terse prime sieve function that generates a potentially infinite sequence of prime numbers ("potentially" because it will run out of memory eventually). Since then, I've used this code many times - mostly because it's short and clear. In this…
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How large is that number in the Law of Large Numbers?
All large numbers are large, but some are larger than others
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The Stack Monoid
(Updated 2020-09-06 with pointers to related work and a bit more explanation)
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Two algorithms for randomly generating aperiodic tilings
[Part of a series: Penrose and hats | Spectres | finite-state transducers | more transducers | refining tilings ]
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How Far Can You Get From McDonald's?
This summer, cruising down the I-5 through California’s Central Valley to the Los Angeles Basin, I unwittingly stumbled upon a most exasperating development: the country strip mall . First, let me state that I don’t hate. I’ve got nothing against Petco, Starbucks, OfficeMax, et al. When overcome by the desire for a…
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What's the difference between 0/0 and 1/0?
From the highly eclectic blog of Mark Dominus
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How Fair Is My D20? (2015)
An automatic system for rolling a polyhedral die and taking photos of the rolls; extracting the image of just the die from those images; clustering the images of the die by which face is shown; and analyzing the results.
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Why are roller coaster loops not circular?
Why are the loops on roller coasters never circular?
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Simulating Wind on Procedural Terrain Using Lattice Boltzmann Method
Note: The full source code for this article can be found here (summarized version). Individual sections contain references to specific code snippets below.
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The expected value of the game is positive regardless of Ballmer’s strategy
A few days ago John Graham-Cumming posted about “Steve Ballmer’s incorrect binary search interview question” which drew a lot of attention on Hacker News. The Ballmer’s favorite brain teaser goes like this:
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Shortest bit sequence that's never been sent over the Internet (2017)
We can never know for sure because we don't have a comprehensive list of all the data. But what can we say probabilistically? Restating it like so:
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The new APT 3.0 solver
APT 2.9.3 introduces the first iteration of the new solver codenamed solver3, and now available with the –solver 3.0 option. The new solver works fundamentally different from the old one. How does it work? Solver3 is a fully backtracking dependency solving algorithm that defers choices to as late as possible. It…