If you write an 878-page treatise revolutionizing all aspects of natural science, from grammar and logic to mathematics, physics, and philosophy, you get a grubby little lane in Oxford.

Solar power on a houseboat on the Thames, near Oxford where this river is still small. Just part of the peaceful walk to Topos UK, where I'm helping David Jaz Myers with his book on category theory for the design of open systems.

Typical brown dwarfs have clouds with a range of molecules from carbon monoxide and methane to more interesting minerals like magnesium silicates and liquid iron. The colder the brown dwarf, the more cloud layers and the more diverse the cloud species. Y dwarfs sit between T dwarfs and Jupiter.

The publisher Springer claims it can only discuss why it retracted Planck's paper with... Planck! But until they hold a seance, they are happy to sell you a completely redacted version: a blank page for $39.95.

In this talk, I explain how to get many of the symmetries of the Standard Model of particle physics from octonionic qutrits. This talk is aimed at particle physicists, full of details - so here let me give you a 'pop' explanation. (1/n)

While France roasted and England sweltered, Scotland had some fine sunny days - a rarety. Tonight, however, a cold fog rolled into Edinburgh.

The Korean branch of Starbucks used AI to create a marketing campaign, but whoops - this campaign celebrated the May 18th massacre of civilians peacefully protesting a military coup in 1980. Result: massive protests and boycotts, legal actions against Starbucks, collapse in stock prices, etc.

The plaque marks the first measurement of the gravitational pull of a mountain. I love it.

What's the deal with derived stacks? Proceeding in steps: A variety or scheme X has a tangent space at each point, and these assemble to form the tangent sheaf TX. If X is smooth this is locally free: a vector bundle. But at singularities, the dimension of the tangent space jumps up! (1/n)

Is topos theory scary? Yes, but only like gorillas are scary.

1/18 A giant underground eye is spying on elusive particles…and it has already made a big result! JUNO — a huge sphere with 20,000 tonnes of transparent liquid buried in China — delivered impressive #antineutrino measurements with its first 59 days of data (late 2025). 🔭🧪⚛️ juno.ihep.cas.cn

This whole picture is a photo! It's the sky as viewed through a 6-meter-wide hole at the top of James Turrell's huge new installation The Dome. The light inside this dome keeps changing - and so does the color of the sky, as the day goes by. People like to lie in the dome and stare up.

When I worked in Singapore at the Centre of Quantum Technologies I went to Cambodia and visited Ta Prohm, an old temple near Angkor Wat. You may have seen it in "Tomb Raider". As nature regains control, it beautifies what it ruins.

Paul Schwahn and I have found a new way to understand the symmetry group of the current best theory of particle physics: the so-called 'gauge group of the Standard Model'. This group is well-known but still mysterious. It seems random. But it's connected to quantum information. (1/n)

Nobody knows how many sets you need to chop up a square and rearrange them to form a circle of equal area!! I'm talking Borel sets - @arula-ratnakar.bsky.social's favorite kind of set. Marks and Unger proved it can be done. Here Marks claims you can do it with ~10²⁰⁰. But how many do you need?

I interviewed Clark Barwick - and in this snippet he sketches how geometries that blend ordinary time with spaces from number theory may let us understand Langlands duality as an equivalence of 4d quantum field theories! It's pretty wild. My mind was blown. youtu.be/t3xkf-hqG2Q?...

Great deal from the local charity shop: a massive two-volume treatise on the steam engine for just 12 pounds. Almost a pound per pound.

The JUNO detector, a huge sphere full of 20,000 tonnes of transparent organic goop, is detecting antineutrinos produced by two nuclear reactors each located the same distance away. After just 2 months, it measured some things about neutrino masses better than ever before! Let's dig in. (1/13)

If I could, I would develop a whole theory linking differential geometry and logic just so I could write a textbook called Truth Tables and Lie Algebras.

An associate editor for Frontiers in Systems Neuroscience has resigned. He asked the editorial office to turn off the AI assistant, and was told it was "not possible". 😵 Read the whole thread!

In general relativity, a point mass just sitting there is inevitably a black hole. But that's when you're living in 3d space (and one dimension of time). In 2d space, a point mass creates a less drastic singularity: a 'cone point'. I've been studying these cone points lately, just for fun. (1/n)

"An Erdős problem resolved by humans! One Abel prize winner was quoted as saying 'We knew the day would eventually come when humans could resolve Erdős problems, but we didn't know it would come this soon!' Several math departments now have plans for workshops on Human Alignment."

According to physicists, a theorem can lead to a strong theoretical prejudice.

The rebellions continue! The publisher Springer put pressure on a journal's editors to accept more papers, just to make more money. The editors resigned and started their own journal, which is peer reviewed and 'diamond open access'. That means FREE to publish in and FREE to read! (1/n)

Oh-oh: Jonas Guan, Tom Blanchard, Hanna Foerster, Hengrui Jia, Gabriel Huang, Nicolas Papernot, AI agents enable adaptive computer worms, arxiv.org/html/2606.03...

Huh. So now the journal Science claims it will retract papers “if the editors determine that a paper’s reported experiments do not support its key conclusions". Does this mean it will retract all papers that are wrong? Or *badly* wrong, whatever that means? It depends on what "support" means!

Hilarious that Marco Rubio was pressured to claim before Congress that these shoes fit him fine.

I think y'all can read this New York Times article. It's worthwhile.

I signed this declaration. leidendeclaration.ai But I had a comment about one passage. (1/n)

I stumbled upon this this morning and I've been staring at it for literally multiple hours today https://sandbox-science.com/particle-life

Why did the 2-holed torus hate the 3-holed torus? Its holier-than-thou attitude.

"What's so great about zines?" "A zine is a magazine without the maga."

you say to yourself "... I'm driving down the road..." but switch the "𝙩𝙝𝙚" to an "𝙖" and say "... I am driving down a road..." and the world opens up [Laurie Anderson] youtu.be/Rlm9xNQkjpA

The sum of the reciprocals of the primes diverges. But to get this sum to reach 6, we need to add up the reciprocals of the first 3 × 10¹³² primes - far more than the number of atoms in the observable universe! Luckily there is no shortage of primes.

With some help from @gro-tsen.bsky.social, Paul Schwahn and I have proved a conjecture connecting the Standard Model to octonions. I'm talking about it on Sunday at 14:30 UTC. I think you can watch it on on Zoom here : aubg-satellite-workshop.netlify.app It probably won't be recorded. (1/n)

MAGA has spectacularly failed to capture musicians. Not only were the bands in the planned "State Fair" mostly minor acts who play in state fairs - most pulled out as soon as they realized what their managers had signed them up for! I want to talk about the Commodores. (Seriously.) (1/n)

The rhombicosidodecahedron has 12 pentagons, 20 equilateral triangles, and 30 squares as faces. Its vertices have coordinates of the form a + b√5 with a,b rational. And if you replace √5 by -√5, the pentagons turn into pentagrams! Here I've only drawn the pentagrams. (1/2)

Make a binary tree listing all matrix products of 1 0 and 1 1 1 1 0 1 If you multiply 1 1 on the left by all these matrices, you get the Calkin-Wilf tree. If you multiply 1 1 on the right by these matrices, you get the Stern-Brocot tree! math.colorado.edu/~kstange/pap...

The new CEO of Wikipedia worked at J.P. Morgan and Lehman Brothers, and now she's firing good people. Wikipedia needs a union now! Sign the petition: en.wikipedia.org/wiki/Wikiped... medium.com/@jakeorlowit...

Take a regular icosahedron. Turn every regular pentagon into a pentagram using a wee touch of Galois theory, and you get... the *great* icosahedron! johncarlosbaez.wordpress.com/2026/05/27/t...

I love canals, so this made me want to do a tour of the midwest US and its half-finished canals - and a boat tour of the finished ones! You can join me on my tour here: mathstodon.xyz/@johncarlosb... A lot of people joined in!

Bad at lab work? Don't give up hope. The man who discovered the electron through some of the most delicate vacuum-tube experiments ever performed was a complete disaster with his hands.

As an abstract group, ignoring its topology, the unit circle is isomorphic to ℚ/ℤ ⊕ ℝ. The first summand contains the roots of unity; the second contains everything else. This is evidence that you should not ignore the topology. And we used the axiom of choice, so maybe that was dumb too.

Coming back from Strasbourg where Alexandre Popoff successfully defended his thesis on categories in music. Decided the French did better at capturing the clanky steampunk charm of escalators: they call them "mechanical stairs". (Escalier mécanique.)

Every PhD thesis applying category theory to music should illustrate the concepts with examples from Batman movies.

Anyone here read Berman and Moody's "The algebraic theory of quasicrystals with five-fold symmetries"? They study an operation called quasiaddition: x⊢y = Φ²x - Φy where Φ = (1+√5)/2. Doing that repeatedly to all the points in the pentagon shown here generates a quasicrystal, they claim! (1/2)

Wow: you can knock out a plant with anesthetics - the same anesthetics that work on people! It's obvious for plants that move, like a Venus fly trap, but experiments have shown it's true for others too. We're still struggling to figure out what this means. pmc.ncbi.nlm.nih.gov/articles/PMC...

Marie Curie, her daughter Irène, and Irène's husband Frédéric all won Nobels on radiation and died of blood cancers. 😢 Marie Curie's notebooks are so radioactive that they may only be opened by people wearing protective suits - and they're stored in lead-lined boxes at the Bibliothèque Nationale!

I never knew what was so great about the "great icosahedron". Now I do! Take a regular icosahedron whose vertices have coordinates in ℚ[√5]. Apply the nontrivial element of the Galois group: that is, replace √5 by -√5. You get the great icosahedron! (1/n)

Asteroid collisions. Downed power lines in thunderstorms. Atomic bomb tests in deserts. These are the only things we know that make quasicrystals outside the lab! johncarlosbaez.wordpress.com/2026/05/14/n...