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Quasi-Polynomial Algorithm for Graph Isomorphism
Update (Dec. 14): The long wait is over! Here’s Laci’s paper on the arXiv. So far, I’ve read it only deeply enough to note that it contains the following sentence: A group G ≤ S…
Most cited
Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 417 posts.
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Trapped priors as a basic problem of rationality
P(A|B) = [P(A)*P(B|A)]/P(B), all the rest is commentary.
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Rathbun's Operator
First, I’m a human typing this post. I’m not going to tell you who I am. Sure, many will say that is cowardly and fair, but I actually don’t think it would bring much value. What matters more is that I describe why, and what I did and didn’t do during the last two weeks or so with the OpenClaw agent I set up, known as…
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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’…
245
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…
246
The Map Is Not the Territory (2015)
The map is not the territory reminds us that our mental models of the world are not the same as the world itself. It cautions against confusing our abstractions and representations with the complex, ever-shifting reality they aim to describe.
247
Ultimate Tic Tac Toe
Once at a picnic, I saw mathematicians crowding around the last game I would have expected: Tic-tac-toe.
248
Deep image prior 'learns' on just one image
Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show that, on the contrary, the structure of a generator network is…
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Eigenvectors and eigenvalues explained visually
Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and even Google's PageRank algorithm. Let's see if visualization can make these ideas more intuitive.
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Human mathematicians are being outcounterexampled
It’s been an interesting few weeks for counterexamples. This post is basically my perspective of what has been going on in the world of formalization, AI tools and, in particular, counterexam…
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Fermat's Last Theorem – how it’s going
So I’m two months into trying to teach a proof of Fermat’s Last Theorem to a computer. We already have one interesting story, which I felt was worth sharing.
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How to learn mathematics: the asterisk method
All original material on the geometry.org website is Copyright (C) 1999–2025, Alan U. Kennington.
256
Reverse Engineering the Hacker News Ranking Algorithm
A data-driven exploration of how the Hacker News ranking algorithm works.
257
The Waiting Time Paradox, Or, Why Is My Bus Always Late?
If you, like me, frequently commute via public transit, you may be familiar with the following situation:
258
Jupyter, Mathematica, and the Future of the Research Paper
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.
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Neural network training makes beautiful fractals
This blog is intended to be a place to share ideas and results that are too weird, incomplete, or off-topic to turn into an academic paper, but that I think may be important. Let me know what you think! Contact links to the left.
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Mastering Linear Algebra in 10 Days: Astounding Experiments in Ultra-Learning
The MIT Challenge My friend Scott Young recently finished an astounding feat: he completed all 33 courses in MIT’s fabled computer science curriculum, from Linear ... Read more
261
Viewing Matrices and Probability as Graphs
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…
262
Lost in Math
Sabine Hossenfelder’s new book Lost in Math should be starting to appear in bookstores around now. It’s very good and you should get a copy. I hope that the book will receive a lot of a…
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Cache Eviction: When Are Randomized Algorithms Better Than LRU? (2014)
Once upon a time, my computer architecture professor mentioned that using a random eviction policy for caches really isn't so bad. That random eviction isn't bad can be surprising — if your cache fills up and you have to get rid of something, choosing the least recently used (LRU) is an obvious choice, since you're…
264
Calculate the day of the week for any date in your head
The Doomsday Algorithm gives the day of the week for any date (and you can do it in your head)
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Number of legal 18x18 Go positions computed. One more to go
L19 = 208168199381979984699478633344862770286522453884530548425639456820927419612738015378525648451698519643907259916015628128546089888314427129715319317557736620397247064840935
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Probabilistic Filters By Example
Probablistic filters are high-speed, space-efficient data structures that support set-membership tests with a one-sided error. These filters can claim that a given entry is definitely not represented in a set of entries, or might be represented in the set. That is, negative responses are conclusive, whereas positive…
267
Is the reversal curse in LLMs real?
A recent paper The Reversal Curse points out an apparent failure in large large language models like GPT-4. From the abstract: We expose a surprising failure of generalization in auto-regressive large language models (LLMs). If a model is
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Understanding the math behind 0x5f3759df and the fast inverse square root (2012)
This post is about the magic constant 0x5f3759df and an extremely neat hack, fast inverse square root, which is where the constant comes from.
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Operation Costs in CPU Clock Cycles
Quote: Back in 80s, it was possible to calculate the speed of the program just by looking at assembly. Another Quote: keep in mind that these days compilers ...
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A Better Strategy for Hangman
Learn the optimal strategy for playing Hangman.