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An OpenAI model has disproved a central conjecture in discrete geometry
An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.
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Sharing AI progress in mathematics
OpenAI publishes new results on open problems in mathematics from an internal frontier model and shares Lean proof formalizations and research details on GitHub.
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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.
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Fable 5.1 Solves the Cyphral Distich, a 370-year-old cipher
Explore Claude Fable 5.1's proposed solution to Sir Thomas Urquhart's Cyphral Distich, a centuries-old cipher, with the reasoning behind the result.
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Formalizing Fermat's Last Theorem
Anthropic is an AI safety and research company that's working to build reliable, interpretable, and steerable AI systems.
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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…
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Compression is prediction
Compression and LLMs are trying to solve the exact same problem: predicting what comes next. Learn the fundamentals of compression and how better prediction leads to better shrinkage.
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You could have invented transformers from memory
Every layer is a memory store
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Two parallel neural ectoderm progenitors contribute to the developing brain
Stanford Health Care delivers the highest levels of care and compassion. SHC treats cancer, heart disease, brain disorders, primary care issues, and many more.
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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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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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Hannah Fry Wins the Leelavati Prize in 2026 for Mathematics Outreach
Hannah Fry is Professor of the Public Understanding of Mathematics in the Department of Applied Mathematics and Theoretical Physics (DAMTP). She joined the University of Cambridge in January 2025, becoming the first person ever to hold the role.
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Decision trees – the unreasonable power of nested decision rules
An introduction to the Decision Trees, Entropy, and Information Gain.
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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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Epoch confirms GPT5.4 Pro solved a frontier math open problem
"A Ramsey-style Problem on Hypergraphs" — a problem from FrontierMath: Open Problems, Epoch AI's benchmark of unsolved research mathematics.
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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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How Shamir's Secret Sharing Works
A visual explanation of how threshold secret sharing lets any k of n shares recover a secret.
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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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Cloudflare targets 2029 for full post-quantum security
Recent advances in quantum hardware and software have accelerated the timeline on which quantum attack might happen. Cloudflare is responding by moving our target for full post-quantum security to 2029.
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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…