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42
In The Hitchhiker’s Guide to the Galaxy by Douglas Adams, the number 42 is the “Answer to the Ultimate Question of Life, the Universe, and Everything”. But he didn’t say wha…
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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Eigenvectors and eigenvalues explained visually
Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and even Google's PageRank algorithm. Let's see if visualization can make these ideas more intuitive.
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The radix 2^51 trick (2017)
Starting from the “ones” position, we add 6 + 6 = 12, write down a 2 and carry a 1. We proceed to the left, one position at a time, until there are no more digits to add.
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Deep Learning Is Applied Topology
Everything lives on a manifold
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0^0
Clever student: I know! $latex x^{0}$ = $latex x^{1-1}$ = $latex x^{1} x^{-1}$ = $latex \frac{x}{x}$ = $latex 1$. Now we just plug in x=0, and we see that zero to the zero is one! Cleverer …
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Steve Wozniak's floating point routines for the 6502
Create beautiful emails, automate campaigns, and track performance. Try it now and see how our tools can drive your business.
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There are only four billion floats, so test them all (2014)
A few months ago I saw a blog post touting fancy new SSE3 functions for implementing vector floor, ceil, and round functions. There was the inevitable proud proclaiming of impressive performance an…
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Human mathematicians are being outcounterexampled
It’s been an interesting few weeks for counterexamples. This post is basically my perspective of what has been going on in the world of formalization, AI tools and, in particular, counterexam…
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Could a modern chess engine on a Pentium have defeated Kasparov in 1996?
A fun experiment where I back-port all the improvements we've made to chess engines over the last 30 years and run it on a 1996 Pentium Pro to see what we could have done if only we knew more at the time.
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I liked this simple calculus exercise
From the highly eclectic blog of Mark Dominus
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How a Kalman filter works, in pictures
I have to tell you about the Kalman filter, because what it does is pretty damn amazing.
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Think in Math, Write in Code
Programmers love to discuss programming languages. We not only debate their technical merits and aesthetic qualities, but they become integrated into our personal identities, along with the values and traits that we associate with them. Some even defend a form of Linguistic Determinism that thinking is confined to…
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A* tricks for videogame path finding
A* Tricks for Videogame Path Finding, A* (A-star) Search Algorithm
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What does randomness look like?
On 13 June 1944, a week after the allied invasion of Normandy, a loud buzzing sound rattled through the skies of battle-worn London. The source of the sound was a newly developed German instrument …
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Neural Networks as Ordinary Differential Equations
Recently I found a paper being presented at NeurIPS this year, entitled Neural Ordinary Differential Equations, written by Ricky Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud from the University of Toronto. The core idea is that certain types of neural networks are analogous to a discretized differential…
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Some Useful Probability Facts for Systems Programming
Probability problems come up a lot in systems programming, and I’m using that term loosely to mean everything from operating systems programming and networking, to building large online services, to creating virtual worlds like in games. Here’s a bunch of rough-and-ready probability rules of thumb that are deeply…
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Bloom filters debunked: Dispelling 30 Years of bad math with Coq
There's this rather nifty feature of modern web browsers (such as Firefox or Chrome ) where the browser will automatically warn the user if they happen to navigate to a " malicious " URL:
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Elliptic Curve Cryptography Explained
Fang-Pen Lin's blog about programming
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Dynamic Programming for Technical Interviews
Probably the first in a multi-part series on DP.
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Understand how transformers work by demystifying the math behind them
Understand how transformers work by demystifying all the math behind them
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I Got a Knuth Check for 0x$3.00
Donald Knuth is a computer scientist who is so committed to the correctness of his books that he offers one US hexadecimal dollar ($2.56, 0x$1.00) for any “bug” found in his books, where a bug is anything that is “technically, historically, typographically, or politically incorrect”. I wanted to get a Knuth check for…
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I can't let go of “The Dunning-Kruger Effect is Autocorrelation”
Organizing my thoughts regarding an argument about the Dunning-Kruger study and statistics in general
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Debunking NIST's calculation of the Kyber-512 security level
[Sidney Harris cartoon used with permission. Copyright holder: ScienceCartoonsPlus.com .]