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Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,394 posts.
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Computational Category Theory in Python III: Monoids, Groups, and Preorders
Parts 1 and 2 are found here and here
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Insert D-Wave Post Here
In the two months since I last blogged, the US has continued its descent into madness. Yet even while so many certainties have proven ephemeral as the morning dew—the US’…
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How medieval astronomers made trig tables
Clever tricks used by medieval astronomers to tabulate sines at every degree, before calculators and before calculus.
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Maximum likelihood estimation and loss functions
When I started learning about loss functions, I could always understand the intuition behind them. For example, the mean squared error (MSE) for regression seemed logical—penalizing large deviations from the ground-truth makes sense. But one thing always bothered me: I could never come up with those loss functions on…
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Homotopy Type Theory and Higher Inductive Types
In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) ci…
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Nonograms: a practical guide with interactive examples
This is a very important technique: only fill cells when you’re certain; no guessing.
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Not so fast, Mr. Fourier
A real explanation of discrete Fourier transform (DFT, FFT), discrete cosine transform (DCT), and their inverses.
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Painting with math: A gentle study of raymarching
A compilation of my Raymarching and Signed Distance Field learnings and work. In it, I teach you how to leverage those techniques along with lighting models, smoothmin, soft shadows, and some math to create beautiful 3D raymarched scenes ranging from abstract shapes to infinite realistic-looking landscapes.
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Dijkstra's Algorithm
I was at SCNA the other day, and someone approached me about TDD and Dijkstra’s algorithm. He wondered if you could find a sequence of tests that would lead you to the algorithm. This sounded like a fun little exercise, so I decided to give it a try here.
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Solving Programming Puzzles Without Using Your Brain
This post is a write-up of a solution to part of a programming puzzle I did yesterday. It’s a little different than the usual “solution + theory” approach, though: I’m going to talk about the actual steps you’d need to take to get to the solution (i.e. what to google, what intermediate code looks like, etc.). Often…
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Smaller than Bloom filters
I've been looking at what would be needed in order to have a global view of CRLs in browsers. At the moment revocation has three problems: privacy (by asking the CA about the status of a certificate you're revealing to them what you're looking at), performance (OCSP checks take hundreds of milliseconds which adds up…
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Strange Attractors (2018)
Interactive Mathematical Applets and Animations
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Learning to solve hard problems in RL for LLMs by never giving up
This is a blog post for my recent paper on RL post-training of LLMs: introducing the Matthew Effect and proposing to solve it with Never Give Up. It is presented interactively and less formally, more like how I give the talk. For a deeper, more technical dive, check out the paper on arxiv and code on github. The…
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Singular Value Decomposition for Programmers
Today's article is a short one. Not because Singular Value Decomposition (SVD) is not important, but because it is so ubiquitous that we'll touch it in other...
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An Algorithm for Polygon Intersections
In this post we'll work our way towards an algorithm that can compute convex polygon intersections. We'll also explore a method for intersections between axis-aligned rectangles, a function that can determine the intersection of two line segments, as well as a point in polygon test.
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Heritability of human life span is ~50% when heritability is redefined
ratios will be ratios
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Loop invariants can give you coding superpowers
A loop invariant is a simple yet powerful tool for designing, testing, modifying, documenting and proving code correct.
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The Math I Learned After I Thought Had Already Learned Math
True story: it’s possible to fly through your own secondary math education — honor roll bumper sticker on your mom’s minivan and all —Â but miss some of the Very Big Ideas of secondary …
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Cylinders in Spheres
What is the largest volume cylinder it is possible to carve from a solid sphere? Also, so you know about the napkin ring problem?
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Constraint Solving with MiniZinc
This is part one of a two-part article. Part two is here. A while back somebody told me to check out MiniZinc. Eventually I did and really enjoyed it, so figured I’d write about it here. This is actually going to be a two part article. Right now we’re talking about what it is and how it works, and in the next post…
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Sets, types and type checking
My currently understanding of types
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A Lisp interpreter implemented in Conway's Game of Life (2021)
Lisp in Life is a Lisp interpreter implemented in Conway’s Game of Life.
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A New Way To Solve Linear Equations (over finite fields)
Impossible but true: a new approach to linear systems Prasad Raghavendra is an expert in many aspects of complexity theory, especially the foundations of approximation theory. He recently was a col…
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Map Simplification with Visvalingam's Algorithm
An interesting challenge in cartography is getting data of the appropriate resolution. As Lewis Fry Richardson observed , the more precisely you measure the length of a coastline, the longer it appears; geographic shapes have infinite complexity. Digital displays, in contrast, are limited by pixels. Choosing too high…