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Visual Cryptography
How to create perfect secret messages that can be decoded using just your eyes.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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Mathematical exploration and discovery at scale
Bogdan Georgiev, Javier Gómez-Serrano, Adam Zsolt Wagner, and I have uploaded to the arXiv our paper “Mathematical exploration and discovery at scale”. This is a longer report on…
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BusyBeaver(6) Is Quite Large
For overdetermined reasons, I’ve lately found the world an increasingly terrifying and depressing place. It’s gotten harder and harder to concentrate on research, or even popular scienc…
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Kelly Criterion – how to calculate optimal bet sizes
So, you’ve probably heard of the Kelly Criterion in the context of gambling or maybe also in the context of investing. When gamblers talk about the Kelly Criterion they are often referring to the idea of sizing your bets, which is the very intuitive idea that if you bet too much of a percentage of your total wealth…
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How Japanese Kids Learn To Multiply
Migliori casino online 2026: confronto bonus, pagamenti e licenze tra i siti più affidabili per giocatori italiani. Guida completa e imparziale.
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A shuffled deck of cards is unique in all human history
Every time you shuffle a deck of playing cards, it's probably a unique order, never before seen in human history.
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I vibed a proof of Conway's conjecture
You can just prove things, apparently.
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Why can’t I go faster than the speed of light?
I should state from the very beginning that the title of this post is a bit of a tease. I don’t know why nothing can go faster than the speed of light. No one does. It is a fundamental pos…
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The Kelly criterion: How to size bets (2019)
Let’s play a game. I have a coin that lands heads 60% of the time and tails 40% of the time. You have $25 and can bet on either side of the coin — every time you’re right you double your bet, and every time you are wrong you lose it.
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Calculating the mean of a list of numbers (2016)
You have a list of floating point numbers. No nasty tricks - these aren't NaN or Infinity, just normal "simple" floating point numbers.
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How hard can generating 1024-bit primes be?
On the one hand they are easy to explain, they are just numbers that have no factors other than one and themselves, but on the other hand they contain endless complexity. They show up in numerous places, ranging from mathematical concepts and conjectures to interesting looking visualizations and cryptography…
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A puzzle that tiles infinitely across both sides, based on the Klein Bottle
Have you ever done a puzzle that has no beginning or end? Where you don’t know up from down? Get lost in the infinite galaxy puzzle. The infinity puzzles™ are a new type of jigsaw puzzle insp…
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Algorithms we develop software by
Pathfinding applied to the software solution domain
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Swift Algorithms
I’m excited to announce Swift Algorithms, a new open-source package of sequence and collection algorithms, along with their related types.
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A quick post on Chen's algorithm
Update (April 19): Yilei Chen announced the discovery of a bug in the algorithm, which he does not know how to fix. This was independently discovered by Hongxun Wu and Thomas Vidick. At present, th…
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Learning Feynman's Trick for Integrals
Among a few other integral tricks and techniques, Feynman's trick was a strong reason that made me love evaluating integrals, and although the technique itself goes back to Leibniz being commonly known as the Leibniz integral rule, it was Richard Feynman who popularized it, which is why it is also referred to as…
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What has a 1 in a million chance? (2010)
If you overheard the phrase "1 in a million chance" in someone else's casual conversation, what might they be talking about?
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The polynomial algorithm for 3-SAT problem (or P=NP)
Dear Fellow Researchers, Would you kindly pay attention to the article “Non-Orthodox Combinatorial Models Based on Discordant Structures” by the author V. F. Romanov published on arXiv.…
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Why don't you use dependent types?
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…
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A faster way to calculate the day of the week
A range of fast modulus techniques that beat compiler output
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The big six matrix factorizations
Six matrix factorizations dominate in numerical linear algebra and matrix analysis: for most purposes one of them is sufficient for the task at hand. We summarize them here. For each factorization …
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Perceptually uniform color spaces
Programming Design Systems is a free digital book that teaches a practical introduction to the new foundations of graphic design.
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L-systems
Jordan Santell, focusing on open web engineering, immersive web, WebXR, WebGL, JavaScript, open source, open standards, and all things weird web.
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D-Wave: Truth finally starts to emerge
Wrap-Up (June 5): This will be my final update on this post (really!!), since the discussion seems to have reached a point where not much progress is being made, and since I’d like to oblige …