Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
We've been speculating for a long time that hash-based keyword lookup ought to be faster than binary search, but up to now we hadn't found a suitable tool for generating the hash function. Joerg Sonnenberger provided the inspiration, and sample code, to show us that rolling our own generator wasn't a ridiculous idea…
The lectures assume no prior knowledge of the Paxos consensus algorithm or of TLA+, the language in which the specifications are written. In fact, the lectures constitute a crash course on TLA+. If you're interested just in the algorithm, you will probably find the specs annoying and will try to read only the…
A description of ECC without using advanced math
GIMPS has discovered a new Mersenne prime number: 2^57885161-1 is prime! Discovered: 2013 Jan 25
A tale of numbers that like to turn: a different look at complex numbers and the strange things they do.
This is the companion website for the paper Understanding Optimization in Deep Learning with Central Flows , published at ICLR 2025.
The other day I ordered a book on art history from Amazon… which reminded me of the movie Angels and Demons , which reminded me of ambigrams. Ambigrams are those stylized words that look the same when you turn them upside down. Here is the classic, by John Langdon .
An introduction into symbolic computations in Python. Don't worry, it's much simpler than it sounds. It's about making Python do your math for you with very little investment in the technology.
The Rule of 72 is a great mental math shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates. Here’s…
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Author’s note: this article used to be called “What Every ComputerProgrammer Should Know About Floating Point, part 1”. Some peoplenoted that this was perh...
In this article I shall discuss several game programming techniques, all revolving around a central theme: the sine and cosine functions. This article will explain sine, cosine, vectors, atan2, and some useful special effects such as how to make homing missiles and how bitmap rotation works. I shall start with the…
Economist. Policy Entrepreneur. Geek. Co-recipient of the 2018 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. University Professor at NYU. Focused on urbanization; cooperation at scale of millions and billions; science; technology; economic development; long-term growth; code as language.
A 100 lines of Python code that substitute the compiler front-end for a specific computation. This shows that you don't need a “fast” compiling language to write efficient code. In fact, a compilation is only one of the multiple ways to achieve speed.
Mathematics, Teaching, & Technology
(Note: this post is `just for fun;’ no premeds, doctors, researchers, or nobel laureates were meant to be offended in the writing of this post.) The bane of many American physics grad student…
Take a look at these two QR codes. Scan them if you like, I promise there's nothing dodgy in them. Left is upper-case HTTPS://EDENT.TEL/ and right is lower-case https://edent.tel/ You can clearly see that the one on the left is a "smaller" QR as it has fewer bits of data in it. Both go to the same URl, the only…
Mathematics with a distinct visual perspective. Linear algebra, calculus, neural networks, topology, and more.
This post is inspired by the “metacademy” suggestions for “leveling up your machine learning.” They make some halfway decent suggestions for beginners. The problem is, thes…
A visual, interactive introduction to hash functions.
The graph, the viewer, and the verification tooling all live in the WeakC4 repository on GitHub .
If vector multiplication were invertible, we could treat vectors just like any other variable. We could do simple algebra like:
Just a brief announcement that I have been working with Quanta Books to publish a short book in popular mathematics entitled “Six Math Essentials”, which will cover six of the fundament…
