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Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
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How does perspective work in pictures?
Why don’t photographs make distant objects big enough?
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Real-world dynamic programming: seam carving
Dynamic programming has a reputation as a technique you learn in school, then only use to pass interviews at software companies. Indeed, most developers do not regularly work on problems where dynamic programming is needed. Ultimately, dynamic programming is a technique for efficiently solving problems that can be…
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The Mathocalypse
More Updates (Oct. 12): Jeffrey Ketchersid has used Claude Code agents to show that BusyBeaver(10) exceeds Graham’s number, beating the previous best result that BB(13) does so. In response t…
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Famous cryptographers’ tombstone cryptogram decrypted
The Sophos Blog
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We're gonna need a lot more mathematicians
[This is a guest post by Amit Sahai. This blog post was initially written in a different file format and converted using AI. — T.] When I was an undergraduate student, I remember talking with…
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U-M finds students with alphabetically lower-ranked names receive lower grades
Knowing your ABCs is essential to academic success, but having a last name starting with A, B or C might also help make the grade.
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Fibonacci Hashing: The Optimization That the World Forgot
I recently posted a blog post about a new hash table, and whenever I do something like that, I learn at least one new thing from my comments. In my last comment section Rich Geldreich talks about h…
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Why recursive data structures?
In this essay, we are going to look at recursive algorithms, and how sometimes, we can organize an algorithm so that it resembles the data structure it manipulates, and organize a data structure so that it resembles the algorithms that manipulate it.
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Think Bayes: Bayesian Statistics Made Simple (2012)
This HTML version of Think Bayes is provided for convenience, but it is not the best format for the book. In particular, some of the math symbols are not rendered correctly.
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Conway's Gradient of Life
What happens if we start from this configuration and take a single step of the game? Here is a snapshot of the next generation:
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I know why the mathematicians weep
On technological grief
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JPEG Compression
JPEG is a clever image compression algorithm that exploits a human perceptual bias and the structure of natural images. It makes a change of basis before encoding so that the rewritten image representation concentrates the signal that humans are most perceptive to, and thus, the remaining details can be discarded…
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Cities: Skylines Is Turing Complete
(Non-clickbait title: building a 4-bit adder in Cities:Skylines.)
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“Burning Ship” fractal
The images described here are generated by analysing the following series for each point (c x ,c y ) on the plane.
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A Primer on Bézier Curves
A detailed explanation of Bézier curves, and how to do the many things that we commonly want to do with them.
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Convolution Is Fancy Multiplication
Like making engineering students squirm? Have them explain convolution and (if you're barbarous) the convolution theorem. They'll mutter something about…
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Second-Order Thinking: What Smart People Use to Outperform (2016)
Second-order thinking is a mental model that smart people like Warren Buffett & Howard Marks use to avoid problems. Read this article to learn how it works.
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Vladimir Voevodsky has died
The Institute for Advanced Study is deeply saddened by the passing of Vladimir Voevodsky, Professor in the School of Mathematics.Voevodsky, a truly extraordinary and original mathematician, made many contributions to the field of mathematics, earning him numerous honors and awards, including the Fields Medal.
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How Shamir's Secret Sharing Works
A visual explanation of how threshold secret sharing lets any k of n shares recover a secret.
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Regex engine internals as a library
Over the last several years, I’ve rewritten Rust’s regex crate to enable better internal composition, and to make it easier to add optimizations while maintaining correctness. In the course of this rewrite I created a new crate, regex-automata , which exposes much of the regex crate internals as their own APIs for…
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Lean proved this program correct; then I found a bug
AI agents are getting very good at finding vulnerabilities in large-scale software systems.
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Statistical Formulas For Programmers
When someone says “7 is greater than 5”, you declare that they’re really the same.