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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.
New
The latest blog posts to take off on Hacker News. 2,851 posts.
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PISA 2025 Students' reading and mathematics performance declined across the OECD
Student performance across OECD countries has continued to decline, reaching the lowest average ever recorded by the OECD Programme for International Student Assessment (PISA) in mathematics and reading. Across the OECD, one in five 15-year-old students is now a low performer in science, mathematics and reading, up…
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Is mathematics about to enter the conservatory?
Math as cultural institution.
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Can guitar frets perform multiplication?
I’m sure that some pictures are worth a thousand words, but others trigger a whole lot of puzzlement. Such was the case with the cover of a book I recently bought entitled Calculating with Tones: The Logarithmic Logic of Music:
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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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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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Poisson Disk Sampling
Stripe Across is a grog. We hope you enjoy it.
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Topologist's Map of the World
Reddit user xilefakamot created this in 2020 — a “topologist’s map of the world.” It depicts international borders and nothing else — the shapes, sizes, and distances between countries are forsaken in order to present the pattern of their borders as efficiently as possible. “No calculations per se – I sketched out a…
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Continuous Diffusion Language Models (CDLM's)
Fully discrete methods dominated for a few years, but language models based on continuous diffusion are making a comeback.
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No country for mediocre mathematicians
White lies of AI from a struggling geometer
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Hilariously fast volume computation with the divergence theorem (2018)
The following presents a fast algorithm for volume computation of a simple, closed, triangulated 3D mesh. This assumption is a consequence of the divergence theorem. Further extensions may generalise to other meshes as well, although that is presently out of scope.
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PageRank explained
Picture this, the year is 1996. You find yourself frustrated with the incumbent search engines like AltaVista, which primarily does a content-based search (it'll give you an article on "Hotels for Chickens" if you search "Hotels" because the word matches). There's gotta be a better way, right? Well, in hindsight, of…
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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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One night in Uzbekistan: Why was this one data point so influential?
We have a comment coming out in Nature next week that is going to cause the retraction of a high-profile paper by Kotz et al. from last year (the second most cited climate paper in the news in 2024).
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Palomar: A registry of Lean verified mathematics
In recent months there has been a proliferation of AI-generated proofs of various old and new results, some of which have been formalized in the proof assistant language Lean. However, checking tha…
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A faster way to calculate the day of the week
A range of fast modulus techniques that beat compiler output
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MathCode, Mathematical Coding Agent
A terminal AI coding agent that formalizes math problems into Lean 4 theorems and proves them.
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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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NP-overrated
If you learned about NP-hard problems in university, your takeaway was probably this:
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A decades-old bug in Knuth's long division (TAOCP Vol II, Algorithm 4.3.1D)
A long division story
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Principia Mathematica is modern and insightful
Notes on Chapter 1 of Principia Mathematica
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What sort of maths are LLMs good at?
For the sake of anyone who might read this blog post in the distant future (a month from now, say), let me mention that I am writing it a few days after OpenAI announced that it had solved ten majo…
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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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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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The lattice of sets of natural numbers is rich (2021)
$\newcommand\of{\subseteq}\newcommand\N{\mathbb{N}}\newcommand\R{\mathbb{R}}\def\<#1>{\left\langle#1\right\rangle}\newcommand\Z{\mathbb{Z}}\newcommand\Q{\mathbb{Q}}\newcommand\ltomega{{{<}…
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Differential Heuristics
In 2005 Google showed off Google Maps, which lets you drag the map around instead of reloading the page like MapQuest and others used. That’s the feature that got everyone’s attention. But what got my attention was a feature they added in 2007 where you could drag the start/end points on a route [1] , and it would…
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There Are Magic Hexagons of Every Order
What is so special about the number 19?
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The Entropy of a Markov Chain
A more explicit example
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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.