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A recent experience with ChatGPT 5.5 Pro
We are all having to keep revising upwards our assessments of the mathematical capabilities of large language models. I have just made a fairly large revision as a result of ChatGPT 5.5 Pro, to whi…
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 163 posts.
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You could have invented transformers from memory
Every layer is a memory store
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AI isn’t outthinking mathematicians, it’s out-remembering them
The key advantage may not be superior reasoning, but a virtually unlimited symbolic working memory.
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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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Could a modern chess engine on a Pentium have defeated Kasparov in 1996?
A fun experiment where I back-port all the improvements we've made to chess engines over the last 30 years and run it on a 1996 Pentium Pro to see what we could have done if only we knew more at the time.
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Nvidia Stock Crash Prediction
One of the questions of the 2026 acx prediction contest is whether Nvidia’s stock price will close below $100 on any day in 2026. At the time of writing, it trades at $184 and a bit, so going down to $100 would be a near halving of the stock value of the highest valued company in the world.
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If math is more than proof, we need to better celebrate the rest of it
[This is a guest post by Grant Sanderson. This blog post was initially written in a different file format and converted using AI. — T.] A sentiment echoing throughout the mathematics communit…
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The Mathocalypse
More Updates (Oct. 12): Jeffrey Ketchersid has used Claude Code agents to show that BusyBeaver(10) exceeds Graham’s number, beating the previous best result that BB(13) does so. In response t…
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We're gonna need a lot more mathematicians
[This is a guest post by Amit Sahai. This blog post was initially written in a different file format and converted using AI. — T.] When I was an undergraduate student, I remember talking with…
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I know why the mathematicians weep
On technological grief
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JPEG Compression
JPEG is a clever image compression algorithm that exploits a human perceptual bias and the structure of natural images. It makes a change of basis before encoding so that the rewritten image representation concentrates the signal that humans are most perceptive to, and thus, the remaining details can be discarded…
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Lean proved this program correct; then I found a bug
AI agents are getting very good at finding vulnerabilities in large-scale software systems.
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Mathematics has changed. Let's act like it
[This is a guest post by Frank Calegari. This blog post was initially written in a different file format and converted using AI. — T.] Why we should not be sad The release by OpenAI on Octobe…
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Missile defense is NP-complete
Exploring the Weapon-Target Assignment problem: how missile defense connects to NP-completeness, SSPK probability calculations, and how saturation attacks exploit computational limits.
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My Mathematical Regression
i become stupid
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You can beat the binary search
We sometimes have to look for a value in a sorted array. The simplest algorithm consists in just going through the values We sometimes have to look for a value in a sorted array. The simplest algorithm consists in just going through the values one by one, until we encounter the value, or exhaust the … Continue reading…
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Improving Heuristics for A* Pathfinding
On my Introduction to A* page I cover the basics of the A* graph search algorithm for finding shortest paths. Here’s an example from the town of Denerim in Dragon Age Origins. Try moving the start and goal to see A* in action:
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Understanding Neural Network, Visually
An interactive visualization to understand how neural networks work
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A digestion of the Jacobian conjecture counterexample
The notorious Jacobian conjecture can be formulated concretely over the complex numbers as follows. Conjecture 1 (Jacobian Conjecture) Let $latex {F:{\bf C}^n \rightarrow {\bf C}^n}&fg=000000$ …
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Conway's Game of Life, in real life
When life gives you switches...
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Optimal Strategy for Connect 4
The graph, the viewer, and the verification tooling all live in the WeakC4 repository on GitHub .
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Six Math Essentials
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…
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Everything is logarithms
Some connections between things, which I have not seen elsewhere. Maybe they mean something?
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The unreasonable effectiveness of the Fourier transform
New : You can now watch a recording of my talk on my YouTube channel ! Or you can just click "play" below, I suppose.
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Quantum Computers Are Not a Threat to 128-Bit Symmetric Keys
There is no need to update symmetric key sizes as part of the post-quantum transition, due to the details of how Grover's algorithm scales. Most authorities agree.
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“Why not just use Lean?”
I have been told that when proposing to formalise mathematics these days, you have to explain why you are not using Lean. And that reminds me why I left the dependent-typed world 40 years ago: its cultism, insularity and conformity. Lean is a great language with good tools, a large library and a huge, enthusiastic…
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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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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. —…