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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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Visualizing quaternions: An explorable video series
Explaining how quaternions, a four-dimensional number system, describe 3d rotation.
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A non-mathematical explanation of one way functions
Alice and Bob are crossword enthusiasts. Every morning they rush to complete the Daily Telegraph cryptic crossword . One morning Alice fini...
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2023 ACM Turing Prize awarded to Avi Wigderson
Avi Wigderson is the recipient of the 2023 ACM A.M. Turing Award for foundational contributions to the theory of computation, including reshaping our understanding of the role of randomness in computation, and for decades of intellectual leadership in theoretical computer science.
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Where is Noether's principle in machine learning?
Physics likes optimization! Subject to its boundary conditions, the time evolution of a physical system is a critical point for a quantity called an action. This point of view sets the stage for Noether's principle , a remarkable correspondence between continuous invariances of the action and conservation laws of the…
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Statistics, we have a problem
Recently, while browsing Twitter, I saw a few machine learning researchers post about an incident at one of their big conferences (NIPS) in…
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Anagram Scoring
From the highly eclectic blog of Mark Dominus
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Creating Shazam in Java
This domain is available for sale. Check out price, information and more on Dovendi.com
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2017 is not just another prime number
Good bye year 2016. Hello year 2017. We all know that 2017 is a prime number, but it is more than just another prime number. 2017π (roun...
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Regular Expression That Checks If A Number Is Prime
Join Illya Gerasymchuk on his new blog as he explores blockchain, DeFi, Zero-Knowledge cryptography, AI, and finance.
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Fast Inverse Square Root
The famous fast inverse square root is some mysterious code not written by programming legend John Carmack to calculate a fast approximation of $1/\sqrt{x}$:
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The Riemann Hypothesis
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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Papers I like
This started out on Twitter and I expected having to write up maybe 50 or so, but then it made the rounds. I don’t think I have 1200+ papers that I’d recommend reading, and even if I di…
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The Mathematical Hacker
The programming profession is blessed with a number of gifted essayists. Today I will pick on three of my favorites — Eric Raymond, Paul Graham, and Steve Yegge — because they all seem to disagree about why (and whether) mathematics is relevant to the practicing programmer. Their attitudes might be summarized as:
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Why do we need human mathematicians anymore?
[This is a guest post by Po-Shen Loh, crossposted from his blog, where an illustrated version appears. This blog post was initially written in a different file format and converted using AI. —…
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Every possible Wordle solution visualized
Every Wordle solution laid out at once. Filter all 2,309 by letter, position, and gray/yellow/green clues to narrow down today's answer.
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Show HN: Interactive Essay on Signals, Sampling and the Fourier Transform
This text is designed to accompany your study of introductory digital signal processing. 1 It’s an eccentric piece of not-so-rigorous literature with a preoccupation for explaining things using interactive visualizations, animations and sound. 2 My goal is to explain the Discrete Fourier Transform using a miniature…
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How Shor's Algorithm works (2007)
I’ve been talking a lot recently about how quantum algorithms don’t work. But last week JR Minkel, an editor at Scientific American, asked me to write a brief essay about how quantum al…
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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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Statistical Mistakes and How to Avoid Them
You can get CS papers published with shoddy statistics, but that doesn’t mean you should. Here are three easy ways to bungle the data analysis in your evaluation section: don’t even try to use statistics when you really ought to; misinterpret an inconclusive statistical test as concluding a negative; or run too many…
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A Lean companion to Analysis I
Almost 20 years ago, I wrote a textbook in real analysis called “Analysis I”. It was intended to complement the many good available analysis textbooks out there by focusing more on foun…
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How you eat corn on the cob predicts whether you're an analyst or algebraist
I like learning about odd connections between disparate things. This probably is the oddest example that I know. Broadly speaking, mathemat...
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All Hail Geometric Algebra
Rotate a cube by 90 degrees around the \(x\)-axis, then rotate it by 90 degrees around the \(z\)-axis. This is equivalent to a single rotation. What is the axis and angle of this single rotation?
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What are skiplists good for?
An exotic data structure and a whole lot of JOINs.
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How Bayesian Inference Works (2016)
Bayesian inference is a way to get sharper predictions from your data. It’s particularly useful when you don’t have as much data as you would like and want to juice every last bit of predictive strength from it.