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The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
Here I’ll try to explain the coolest ideas in each of AlphaProof’s IMO 2024 solutions. AlphaProof produces proofs in Lean, and each Lean proof is composed of a series of tactics. So I’ll pick out the tactics that correspond to these ideas in the proofs for problems 1, 2 and 6 (the three problems that AlphaProof…
StarCraft pathfinding looked impossible to fix until one ugly hack changed everything. Here's the trick that shipped.
How do you make an accurate machine without one to copy? Explore flat surfaces, screw-cutting lathes, and millionth-of-an-inch measurements through interactive 3D figures.
Where noise hides when deep neural networks generalize.
Attempting to model modern dating using the lessons learned from the stable marriage problem
The OpenAI algorithm for the FFT is less a breakthrough and more a malicious exploit.
Finally! On May 19, 2022, GitHub released one of its most requested features: Math support on Markdown! Many had been anticipating this for years, including myself, so much in fact that I wrote a browser extension to get there early. (xhub, it can do a few other things so check it out.)
If you learned about NP-hard problems in university, your takeaway was probably this:
Our geometric intuition developed in our three-dimensional world often fails us in higher dimensions. Many properties of even simple objects, such as higher dimensional analogs of cubes and spheres, are very counterintuitive. Below we discuss just a few of these properties in an attempt to convey some of the weirdness…
An explanation of the forms of mathematics I use on a daily basis as a working software engineer.
I made a New Year's resolution: every plot I make during 2018 will contain uncertainty estimates. Nine months in and I have learned a lot, so I put together a summary of some of the most useful methods.
A Bloom filter is a data structure designed to tell you, rapidly and memory-efficiently, whether an element is present in a set.
How do you find near-duplicates in a massive collection of documents? An exploration of the Jaccard similarity metric, and the MinHash hashing trick used to efficiently approximate it at web scale.
I discuss several commonly held perspectives on the complex numbers and explore how their differences engage with several aspects of structuralism in the philosophy of mathematics.
Almost all mathematical questions one could have about Wordle are settled by now. I summarize here what is known so far.
Cut out everything that's not surprising.
Let's chill just a little bit on the "TLA+ will save AI from itself" narrative
`atan2f` is an important but slow trigonometric function. In this article we'll explain how to approximate it, and implement a version 50x faster than `glibc` on batches of inputs.
There are few things I think about more than the essays on gwern.net, and there are few with as satisfying a theoretical payout to contemplate in my orb as his essay on “leaky pipelines”, aka log-normal distributions. The skulk: Say you’re working on a Laravel web app. You’re about 90% sure you know how to start the…
Today I'd like to share an idea. It's a very simple idea. It's not fancy and it's certainly not new. In fact, I'm sure many of you have thought about it already. But if you haven't—and even if you have!—I hope you'll take a few minutes to enjoy it with me. Here's the idea: Every matrix corresponds to a graph. So…
A list of things that were not supposed to be Turing-complete, but are.
A couple of Sundays ago, I wrote an implementation of Dijkstra’s algorithm in Clojure. The core algorithm came to twenty-five lines. I banged out the code as...
What do revolutionary new Sudoku techniques teach us about real-world problem solving?
I’m trying to get into neural networks. There have been a couple big breakthroughs in the field in recent years and suddenly my side project of messing around with programming languages seeme…
I have a confession to make: I have always found symbolic algebra more intuitive than geometric pictures. I think you’re supposed to feel the opposite way, and I greatly admire people who think and communicate in pictures, but for me, it’s usually a struggle.
