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Knuth changes his mind on Bernoulli number B_1
(I thank Yoshiyuki Kotani for this identity. We'll be able to use the same idea again in 2024 and 2027!)
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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Dynamic Progamming: First Principles
Many problems of todays world require multiple decisions made throughout the lifetime of the problem. Choices are made based upon information, including previous decisions made in the problem. This article looks at how Dynamic Programming can be applied to help solve these problems in an efficient manner.
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The game of life emulated in the game of life
Conway's Game of Life, emulated in Conway's Game of Life: The life simulator used is Golly which has a built-in script to generate these metapixel grids (select a pattern, and choose "metafier.py" from the scripts list). Outer Totalistic Cellular Automata Meta-Pixel: The metacell uses a period 184 tractor beam, which…
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TurboQuant: A first-principles walkthrough
Each mini-demo below covers one concept used later. Skip the ones you already know.
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A high-dimensional sphere spilling out of a high-dimensional cube
Make a square, split each side into two halves, producing four cells. Put a circle into each cell such that it fills it completely. There is a small gap right in the middle of the square. Put a circle there again such that it touches the other four circles. The central circle is obviously inside the square, right?…
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Queueing theory: The science of waiting in line
The math behind how people wait in line
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A Programmer’s Intuition for Matrix Multiplication
What does matrix multiplication mean? Here's a few common intuitions: This is useful when first learning about vectors: vectors go in, new ones come out.…
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Thoughts about what worked in math circles
Thoughts about what worked in math circles After about 7 months of math circles with a group of 7- turning 8-year-old boys and girls, I decided to take a...
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California needs real math education, not gimmicks
A guest post by Armand Domalewski.
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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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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…
377
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
379
Creating Shazam in Java
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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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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…