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Penrose: From mathematical notation to beautiful diagrams
Materials from our SIGGRAPH '20 paper.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 460 posts.
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Algebraic Semantics for Machine Knitting
As programming languages researchers, we’re entitled to a certain level of mathematical rigor behind the languages we write and analyze. Programming languages have semantics , which are definitions of what statements in the language mean. We can use those semantics to do all sorts of useful things, like error…
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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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Michael Atiyah has died
We are very sorry to hear of the death of Michael Atiyah. Michael was a giant of mathematics. He held many positions including Savilian Professor of Geometry here in Oxford, President of the Royal Society, Master of Trinity College, Cambridge, the founding Directorship of the Isaac Newton Institute and Chancellor of…
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Penrose 3.0
Create beautiful diagrams just by typing math notation in plain text.
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PageRank algorithm for graph databases
What is PageRank algorithm? How can it be used in various graph database use cases? How to use it in Memgraph? If these questions are keeping you up at night, here is a blog post that will finally put your mind at ease.
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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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Communicating Advanced Mathematics to Kids
I’ve often thought that we could do a lot better job of explaining “advanced” mathematics concepts in simple language for the benefit of a wider audience. As a student, I never liked being told, “We’ll explain that to you next year.” As a teacher, I’ve always wanted be able to give real answers to students’…
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Progress toward fusion energy gain as measured against the Lawson criteria
Today we’ve released a pre-publication version of an update to our 2022 paper “Progress toward fusion energy breakeven and gain as measured against the...
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First improvement of fundamental algorithm in 10 years
The max-flow problem, which is ubiquitous in network analysis, scheduling, and logistics, can now be solved more efficiently than ever.
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There's Math.random(), and then there's Math.random()
V8’s Math.random implementation now uses an algorithm called xorshift128+, improving the randomness compared to the old MWC1616 implementation.
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Claude Shannon: The Mathematical Theory of Cryptography
The foundation of modern cryptography.
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The Boyer-Moore Fast String Searching Algorithm
Our algorithm has the peculiar property that, roughly speaking, the longer the pattern is, the faster the algorithm goes. Furthermore, the algorithm is ``sublinear'' in the sense that it generally looks at fewer characters than it passes. The algorithm is described in
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Crooked to the Millimetre
The technology pioneered by the ETH spin-off incon.ai allows blocks to be positioned with pinpoint accuracy, creating structures with aesthetic designs and augmented acoustics.
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When Bloom filters don't bloom
Last month finally I had an opportunity to use Bloom filters. I became fascinated with the promise of this data structure, but I quickly realized it had some drawbacks. This blog post is the tale of my brief love affair with Bloom filters.
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Math writing is dull when it neglects the human dimension
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
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Ace of Aces: Why you should do maths as a game designer
Every now and again you come across something that stretches your brain in a new direction. Last week I stumbled on a magic trick of a Choose Your Own Adventure: Al Leonardi’s Ace of Aces, a paper …
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Analyzing the chords of 1300 popular songs for patterns
Discover the secrets behind hit music with our popular song chords analysis from 1300 tracks. Your songwriting journey begins here!
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(Very) Basic Intro to Elliptic Curve Cryptography
Learn cryptography in Go by building ciphers, hashes, password security, and encryption tools. Understand security beneath the library call.
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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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The faster-than-fast Fourier transform
For a large range of practically useful cases, MIT researchers find a way to increase the speed of one of the most important algorithms in the information sciences.
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The Riemann Hypothesis Says 5040 Is the Last
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…