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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.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 41 posts.
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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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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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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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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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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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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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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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Quantization from the Ground Up
A complete guide to quantization: how LLMs store parameters as floats, why shrinking them to 4 or 8 bits barely hurts accuracy, and how to measure the tradeoff.
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Navier-Stokes Announcement
The Millennium Prize Problems were unveiled by the Clay Mathematics Institute (CMI) at a meeting in Paris in 2000 to celebrate “The Universality of Mathematical Thought”. These problems encapsulate some of the most difficult challenges that mathematicians were grappling with at the turn of the millennium. CMI’s…
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What are skiplists good for?
An exotic data structure and a whole lot of JOINs.
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Learning more about Claude's mathematical capabilities
An unreleased Claude model improved the lower bound for the fraction of zeroes of the Riemann zeta function that satisfy the hypothesis, raising it from 41.6% to 67.2%.
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Dust: Pretraining Transformers Without Backpropagation
Deep learning has been built around backprop, the only credit assignment algorithm capable of training modern neural nets, including transformer-based language models. Backprop requires differentiability and produces first-order gradients, and deep learning’s architectures, optimizers, and hardware have co-evolved…
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Scientists observe Einstein's gravity in the quantum world
An international team including Oxford physicists has observed a long-predicted effect of gravity on a falling quantum object for the first time. The study provides an experimental connection between quantum physics and Einstein's theory of gravity.
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Bijou64: A variable-length integer encoding
An accidentally fast variable-length integer encoding
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Simons Foundation launches $15M effort to help mathematicians navigate AI era
The Simons Foundation today announced a new set of initiatives that will help the mathematics community navigate the rapid rise of artificial intelligence in the field. Under a partnership…
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Introduction to Formal Verification with Lean Part 1
A tutorial Formal Verification using Lean for cryptographic engineers. Implement and prove correctness of the One-Time pad following a cryptography book.
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Progress on provable inference for large language models
Sharing progress on a powerful type of cryptographic proof known as a zkSNARK, which is uniquely fit for provable inference.
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Upper stage impacting the moon on 2026 August 5
On 2026 August 5, within a few minutes of 06:35 UTC, an upper stage (section) of a rocket used for a lunar mission will hit the moon. This may be of some (probably minor) scientific interest, and we may learn some things from it. It doesn't present any danger to anyone, though it does highlight a certain carelessness…
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Sampling at negative temperature
Summary : Inspired by the definition of temperature in statistical mechanics and the possibility for it to be below zero, we try sampling LLaMA at T = − 0.001 T=-0.001 T = − 0.001 . The results are maximally weird.
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Are arrays functions?
A high-performance and high-level purely functional data-parallel array programming language that can execute on the GPU and CPU.
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Jean-Pierre Serre turns 100
Jean-Pierre Serre is a French mathematician who has made important contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was a member of Bourbaki.
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More than half of adults in U.S. say they lack basic statistical understanding
Many people in the U.S. believe that their statistical knowledge is limited, but they would rely on statistics for decision-making more if they understood statistics better, according to a new study led by a Penn State researcher.
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John Coltrane illustrates the mathematics of jazz
The Jazz of Physics: Albert Einstein and John Coltrane had a lot in common. The so-called “Coltrane circle” or “Circle of Fifths,” but incorporates Coltrane’s own innovations. Coltrane gave the drawing to saxophonist and professor Yusef Lateef in 1967, who included it in the Repository of Scales and