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Bicycle
Interactive article explaining the physics of a bicycle.
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4B If Statements
I recently stumbled upon this screenshot while researching social media on the train. Of course, it was followed by a cascade of spiteful comments, criticizing this fresh programmer’s attempt to solve a classical problem in computer science. The modulus operation.
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Math breakdown: Anime homing missiles
Tech Notes on Cubic Bezier Curves, Perlin Noise, and Minimal Rotation Frames
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Refusing to teach kids math will not improve equity
We have public schools for a reason.
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A non-mathematical introduction to Kalman filters for programmers
Read my manifesto on Code as an alternative to Mathematics. Code for this article can be found on this Colab Notebook should you choose to follow along. Why Kalman Filters? Kalman filters are ingenius. If you have never heard of them, then a very intuitive (and arguably reductive) way to think about them is to
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The Dunning-Kruger effect is autocorrelation
Do unskilled people actually underestimate their incompetence?
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Reverse engineering a neural network's clever solution to binary addition
While training small neural networks to perform binary addition, a surprising solution emerged that allows the network to solve the problem very effectively. This post explores the mechanism behind that solution and how it relates to analog electronics.
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I liked this simple calculus exercise
From the highly eclectic blog of Mark Dominus
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Debunking NIST's calculation of the Kyber-512 security level
[Sidney Harris cartoon used with permission. Copyright holder: ScienceCartoonsPlus.com .]
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U.S. stock market returns – a history from the 1870s to 2022
Facts and figures on U.S. stock market returns from 1871 to 2024. Annual returns, likelihood of losing money, best / worst months, and more.
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37, the median value for the second prime factor of an integer
Chris Grossack's math blog and professional website.
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Google’s fully homomorphic encryption compiler – a primer
Back in May of 2022 I transferred teams at Google to work on Fully Homomorphic Encryption (newsletter announcement). Since then I’ve been working on a variety of projects in the space, including being the primary maintainer on github.com/google/fully-homomorphic-encryption, which is an open source FHE compiler for…
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Do Machine Learning Models Memorize or Generalize?
An interactive introduction to grokking and mechanistic interpretability.
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NIST Elliptic Curves Seeds Bounty
Announcing a $12,288 bounty (tripled to charity) for cracking the five seeds selected by the NSA in the '90s for the NIST elliptic curve standard.
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Decomposing language models into understandable components
Interpretability research decomposing a transformer layer into thousands of interpretable features that can steer model behavior.
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Functions are vectors
Conceptualizing functions as infinite-dimensional vectors lets us apply the tools of linear algebra to a vast landscape of new problems, from image and geometry processing to curve fitting and machine learning.
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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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FunSearch: Making new discoveries in mathematical sciences using LLMs
We introduce FunSearch, a method for searching for “functions” written in computer code, and find new solutions in mathematics and computer science. FunSearch works by pairing a pre-trained LLM, whose goal is to provide creative solutions in the form of computer code, with an automated “evaluator”, which guards…
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Beautiful branchless binary search
I read a blog post by Alex Muscar, “Beautiful Binary Search in D”. It describes a binary search called “Shar’s algorithm”. I’d never heard of it and it’s i…
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Why do prime numbers make these spirals? (2019)
A curious pattern in polar plots with prime numbers, together with discussion of Dirichlet's theorem
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A regular expression to check for prime numbers (2007)
Regular expressions are extremely powerful. This is something I read at least once or twice every day while reading articles and blogs on the Web.
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He made linear algebra fun
Mathematics Professor Gilbert “Gil” Strang taught his last class to thousands after teaching calculus, analysis, and linear algebra for more than 60 years at MIT and online. He reflects on his life at the Institute and as an instructor with MIT OpenCourseWare.
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Let's try to understand AI monosemanticity
Inside every AI is a bigger AI, trying to get out
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Fundamental Math for Game Developers
Let's review the most important math topics used by game devs, reflect about math education, and discuss techniques that can be used to improve the way we learn new math topics.
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Why does 0.1 and 0.2 = 0.30000000000000004?
Why does 0.1 + 0.2 = 0.30000000000000004?
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π in Other Universes
How the value of π depends on the definition of distance.