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Conterintuitive facts in mathematics, CS, and physics
It is possible to compute over encrypted data without access to the secret key: https://en.wikipedia.org/wiki/Homomorphic_encryption
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Poisson's Equation
If you aren’t used to staring at math, Poisson’s equation looks a little intimidating:
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Functorio
You might have heard people say that functional programming is more academic, and real engineering is done in imperative style. I’m going to show you that real engineering is functional, and …
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How percentile approximation works and why it's more useful than averages
What percentile approximations are, how percentiles work in PostgreSQL, and calculating them efficiently on time-series data.
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The solution of the Zodiac killer’s 340-character cipher
See how Mathematica was used to solve one of the cryptograms sent in a letter by the Zodiac Killer.
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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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Solving NP-hard puzzles with the oldest trick in the book
KOITOTO hadir dengan mengutamakan kemudahan akses serta dukungan bagi pengguna yang membutuhkan informasi seputar layanan dan navigasi situs.
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That XOR Trick (2020)
There are a whole bunch of popular interview questions that can be solved in one of two ways: Either using common data structures and algorithms in a sensible manner, or by using some properties of...
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Quaternions
Introduction to quaternions and rotations in 3D.
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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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How to learn mathematics: the asterisk method
All original material on the geometry.org website is Copyright (C) 1999–2025, Alan U. Kennington.
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State machines are wonderful tools
I love when my current problem can be solved with a state machine. They’re fun to design and implement, and I have high confidence about correctness. They tend to:
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What is the inverse of a vector?
If vector multiplication were invertible, we could treat vectors just like any other variable. We could do simple algebra like:
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What3Words – The Algorithm
What3Words is a widely promoted system that is used for sharing a location using just three words. For example, ///wedge.drill.mess is located in Hyde Park.The globe is divided into 3m squares, eac…
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Functorio
You might have heard people say that functional programming is more academic, and real engineering is done in imperative style. I’m going to show you that real engineering is functional, and …
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An Interactive Guide to the Fourier Transform (2012)
The Fourier Transform is one of the deepest insights ever made. Unfortunately, the meaning is buried within dense equations:
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An alarming trend in K-12 math education: a guest post and an open letter
Updates: Our open letter made the WSJ, and has been tweeted by Matt Yglesias and others. See also Boaz Barak’s thread, and a supportive tweet from Rep. Ro Khanna (D-Silicon Valley). If you…
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Did Schnorr destroy RSA? Show me the factors
Schnorr has claimed new factoring methods that “destroy RSA”. This should be easy to demonstrate with well known challenges.
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SoME1 results
Reflections on the Summer of Math Exposition
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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…