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Simpson’s Paradox (2016)
A riveting tale of how good data can lead to bad decisions.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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GIMPS Project Discovers Largest Known Prime Number
Discovery of the 50th known Mersenne Prime.
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Modern SAT solvers: fast, neat and underused
Before I started doing research, I saw SAT solvers as academically interesting but without practical uses ouside of other academic applications. I've since then changed my mind, and I want to change yours, because modern SAT solvers are neat, fast and almost criminally underused by the industry.
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Making any integer with four 2s
There's a cute math puzzle that can be interesting to folks on very different levels:
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The Inconsistency of Arithmetic (2011)
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
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Language models pack billions of concepts into 12k dimensions
In a recent 3Blue1Brown video series on transformer models, Grant Sanderson posed a fascinating question: How can a relatively modest embedding space of 12,288 dimensions (GPT-3) accommodate millions of distinct real-world concepts? The answer lies at the intersection of high-dimensional geometry and a remarkable…
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Kalman Filter Explained Simply
Tired of equations and matrices? Ready to learn the easy way? This post explains the Kalman Filter simply with pictures and examples!
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A Beginner's Guide to Understanding Convolutional Neural Networks
Engineering at Forward | UCLA CS '19
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2+1=4, by quinoa
I was struck the other day by the following: The cooking instructions on my Bob’s tri-colored quinoa package said to combine 2 cups of water with 1 cup of dried quinoa, which would ultimately create 4 cups of cooked quinoa. See image above. My first reaction was to believe …
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Just A New Fractal Detail In The Big Picture (2015)
When the central heating takes effect I'll get up and make myself some tea and porridge to which I'll add some nuts and fruit. I'll switch on The World Service to hear the news, and then make a few phone calls about damp-proofing. And I'll probably plant the daffodil bulbs for Spring (it says on the packet they should…
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A neat XOR trick
Looking over the solutions mega-thread , it seems like not many people discovered this trick; when I posted about it , people found it to be noteworthy.
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Image Kernels explained visually
An image kernel is a small matrix used to apply effects like the ones you might find in Photoshop or Gimp, such as blurring, sharpening, outlining or embossing. They're also used in machine learning for 'feature extraction', a technique for determining the most important portions of an image. In this context the…
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Using Fibonacci numbers to convert from miles to kilometers and vice versa
I recently learned an interesting fact about Fibonacci numbers while watching a random number theory video on YouTube. Fibonacci numbers can be used to approximately convert from miles to kilometers and back. Here is how. Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No...
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Images Created from Prime Numbers
Inspired by James McKee’s Trinity Hall prime, physics researcher Gilles Esposito-Farese (of the self-descriptive pangram) has worked out that this 2,258-digit prime number: 53084469288402965415857953902888840109250315594591772197851275320 59910735745658243457138160802170063601085186072703319516241231606…
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Visual Sum of Cubes
This article discusses a ‘visual’ derivation of the formula for 1³+2³+…+n³.
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You can beat the binary search
We sometimes have to look for a value in a sorted array. The simplest algorithm consists in just going through the values We sometimes have to look for a value in a sorted array. The simplest algorithm consists in just going through the values one by one, until we encounter the value, or exhaust the … Continue reading…
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Algorithms on Khan Academy – a collaboration with Dartmouth College professors
What is an algorithm ? It’s a sequence of steps that you follow to solve a problem. In everyday life, you might have an algorithm for hangin...
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Biggest image in the smallest space
What’s the biggest pixel size of a PNG image in the smallest number of bytes? I wanted to try to create an image that could be downloaded but whose pixel buffer would be too big to store in the RAM of a PC. Here is a PNG image of 6,132,534 bytes (5.8 MB) and 225,000 × 225,000 pixels (50.625 gigapixels), which, if…
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Translating math into code with examples in Java, Racket, Haskell, Python (2011)
These structures are so universal that most research papers in the theory of computation, programming languages and formal methods present concepts in terms of discrete mathematics rather than code.
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Generating sudokus for fun and no profit
A guide on how to generate sudokus of any difficulty.
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Feynman’s Razor
If an expert can't understand your explanation, you've dumbed it down too much!
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Why deep learning works even though it shouldn’t
Why models always get better when they are bigger and deeper, even when the amount of data they consume stays the same or gets smaller.
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