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On the Navier–Stokes Millennium Prize Problem
We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.
Most cited
Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 20 posts.
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A global workspace in language models
Interpretability research on Claude's internal thoughts.
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Emotion concepts and their function in a large language model
All modern language models sometimes act like they have emotions. What’s behind these behaviors? Our interpretability team investigates.
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The Dunning-Kruger effect may just be a data artefact (2020)
I want the Dunning-Kruger effect to be real. First described in a seminal 1999 paper by David Dunning and Justin Kruger, this effect has been the darling of journalists who want to explain why dumb people don’t know they’re dumb. There’s even video of a fantastic pastiche of Turandot’s famous aria, Nessun dorma…
5
Artemis II is not safe to fly
On Wednesday, NASA will attempt to send four astronauts around the moon on a mission called Artemis II. This will be second flight of NASA’s SLS rocket, and the first time the 20-year-old Orion capsule flies with people on board.
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When AI Builds Itself: Our progress toward recursive self-improvement
Our progress toward recursive self-improvement, and its implications.
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A cryptography engineer's perspective on quantum computing timelines
The risk that cryptographically-relevant quantum computers materialize within the next few years is now high enough to be dispositive, unfortunately.
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Good sleep, good learning, good life (2012)
The good educator insists on exercise, play, and plentiful sleep: "the great cordial of nature."
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Quantum computing bombshells that are not April Fools
For those of you who haven’t seen, there were actually two “bombshell” QC announcements this week. One, from Caltech, including friend-of-the-blog John Preskill, showed how to do quantum faul…
10
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…
11
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 $latex {F:{\bf C}^n \rightarrow {\bf C}^n}&fg=000000$ …
12
The case against geometric algebra (2024)
Every once in a while the internet gets talking about Geometric Algebra (henceforth GA) and how it’s a new theory of math that fixes everything that’s wrong with linear algebra and multivariable calculus. When I come across this stance I am compelled to respond with something like: “wait wait, it’s not true! GA is…
13
Kraków, Poland in top 5 worst air quality worldwide
Compare live air quality rankings for major cities worldwide. See real-time AQI levels and pollution conditions by location.
14
Ten advances in mathematics and theoretical computer science
OpenAI shares new results on long-standing open problems in mathematics and theoretical computer science, including advances in geometry, cryptography, and complexity.
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An old patent inspired the new "Y-zipper", a three-sided fastener
A new system developed at MIT CSAIL helps users design three-sided fasteners called “Y-zippers,” then 3D prints them. The devices can be attached or embedded to camping equipment, medical gear, robots, and art installations, seamlessly switching each item between soft and rigid.
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Nicholas Polson has authored 258 academic papers in 2026 so far
Nicholas Polson has, by my count using his SSRN page, already written 258 working papers in 2026 alone. He’s already written (or at least published to SSRN), six papers today, August 26, 2026.
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The Singularity will occur on a Tuesday
src= alt="Always has been astronaut meme" / "Wait, the singularity is just humans freaking out?" "Always has been." Everyone in San Francisco is talking about t
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GPT-5.2 derives a new result in theoretical physics
A new preprint shows GPT-5.2 proposing a new formula for a gluon amplitude, later formally proved and verified by OpenAI and academic collaborators.
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Where to Find the Colors Your Screen Can't Show You
An atlas of the vibrance of the real world
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When Kitty Litter Caused a Nuclear Catastrophe
[Note that this article is a transcript of the video embedded above.] Late in the night of Valentine’s Day 2014, air monitors at an underground nuclear waste repository outside Carlsbad, New Mexico, detected the release of radioactive elements, including americium and plutonium, into the environme