When you repeatedly measure the positions of over a billion stars so accurately that you can see a star moving by an amount equal to the size of a pinhead on the Moon, as seen from Earth... you find amazing things! It's great. mathstodon.xyz/@johncarlosb...

Lise Meitner, who discovered nuclear fission and did the experiments that led Pauli to postulate neutrinos, is one of my heroes. She had to work twice as hard for everything, and did so much. I tell a bit of her story here: mathstodon.xyz/@johncarlosb...

In quantum mechanics we say how an observable O(t) changes using the Heisenberg equation. But what if you've just got a Jordan algebra? No i, no commutator, just the Jordan product ∘. Then dO(t)/dt = {A, O(t), B} where {A,O,B} = (A∘O)∘B - A∘(O∘B). 😮 golem.ph.utexas.edu/category/202...

Paulina Borsook got it before the rest of us: "Every day, computers are making people easier to use." mathstodon.xyz/@gilduran.co...

Anthropic owes me - and my coauthors, and publishers - $9000 for books they ripped off. Check out the list and see how much they owe you: secure.anthropiccopyrightsettlement.com/lookup Details on how this works: authorsguild.org/advocacy/art...

Write it down in your calendar! The big annual applied category theory conference, ACT2026, is happening in Tallinn, Estonia, 6–10 July, 2026, right after the Adjoint School Research Week, which is 29 June – 3 July. More info here: actconf2026.github.io/index.html

A time-reversed black hole would be a 'white hole'. It has an 'anti-horizon' that you can only fall *out* of! In this video, Philip Gibbs answers some of the most fascinating questions about white holes. johncarlosbaez.wordpress.com/2025/10/27/p...

Can you help? I'm trying to find this fascinating paper in a rather obscure journal, with no luck so far.

Just so you know: this claimed proof of P≠NP is a bunch of baloney. Written with help of an LLM, it's internally inconsistent and at least one step is clearly wrong. arxiv.org/abs/2510.17829

It's our best theory of elementary particles and forces. It took centuries of genius to discover that the world is like this, and it's absolutely shocking. But nobody believes it's the last word, so we simply call it The Standard Model. I will try to explain it... www.youtube.com/watch?v=0yjx...

This depends so much on the definition of "we". (Free book here: sci-books.com/do-we-really... )

A novel Jules Verne wrote in 1863 about Paris in 1960, which appeared only in 1994. A world with a computer network, fax machines... a world where commerce and industry reign supreme, and the arts can be damned. www.youtube.com/watch?v=XckA...

While this has outraged many people, authorities have appealed to the French public to just "accept it". waterfordwhispersnews.com/2025/10/20/l...

My story of using Claude to solve a math problem. I don't think it sped up my solution of the problem, but it was rather interesting. It was like having a bumbling, sometimes insightful, sometimes deceitful, but always cheerful and eager assistant. mathstodon.xyz/@johncarlosb...

I'm giving four talks this fall, so if you're in Edinburgh or Cambridge please stop by! Cospans of finite sets (twice), using category theory to build software for modeling in epidemiology, and the cobordism hypothesis. Details here: mathstodon.xyz/@johncarlosb...

Aisuru now launches distributed denial-of-service (DDoS) attacks of almost 30 terabits per second! And it keeps growing. mathstodon.xyz/@johncarlosb...

You can get the periodic table from a quantum field theory! At least approximately. The first element that doesn't follow the pattern is chromium. But it works pretty well. mathstodon.xyz/@johncarlosb...

250 documents with a keyword followed by gibberish, injected into the training of a large language model, can "poison" it - according to Anthropic. www.anthropic.com/research/sma...

It must have been so fun to first discover 'cathode rays' - now called electrons - and then 'anode rays' - positive ions, including protons - like this. Crank up the voltage on an evacuated tube and get weird glows!

Wow, it seems a black hole fell into a star and quickly at it all up, producing 3 big gamma ray bursts! First time we've seen this. As I explain, it may have been a 'helium star': a blue giant star that had shot off all its outer layers, leaving its helium core. mathstodon.xyz/@johncarlosb...

People who don't like dark matter have probably never thought about how hard it would be to go beyond the Standard Model without some clue like dark matter. A good theory might explain dark matter and also *simplify* the Standard Model. Simpler theories often have more particles.

Swirl: a swirling piece of music from my album Treq Lila, made by "breeding" cellular automata in Steve Wolfram's WolframTones system: soundcloud.com/john-c-baez/... Art by Greg Egan.

My crazy new hope about quantum logic is that it's been inconsequential for "real-world physics" mainly because we haven't gone far enough down the rabbit-hole. I am now going down the rabbit-hole. (Vinberg's special T-algebras, here I come!)

Grothendieck wrote of how the gradual buildup of results in algebraic geometry is like a slowly rising sea. But from the student's perspective, it looks like this. 😆

Susumu Kitagawa, Richard Robson and Omar M. Yaghi won the Nobel prize in chemistry for metal-organic-frameworks! These are molecular structures built from metal atoms and organic compounds, full of microscopic holes. One gram can have a surface area of more than 12,000 square meters!

If I made a series of videos about something, what would you like? The Standard Model? Grand unified theories? Clifford algebras? The octonions? Entropy? Category theory? Quantum logic and projective geometry? Visually beautiful math?

Грег Иган looks like the name of an alien supervillain.

A while back I noticed that *roughly* speaking, the Standard Model gauge group is the group of transformations of an octonionic qutrit that preserve both an octonionic qubit and a complex qutrit. But I'm still working on the math of this. golem.ph.utexas.edu/category/202...

Students who *memorize* organic chemistry consider it torture. But to *explore* is a delight. It's like the difference between being force-fed and enjoying a buffet. Yesterday I learned about 'crown ethers': beautiful crown-shaped molecules. Check 'em out! mathstodon.xyz/@johncarlosb...

Chemistry is so fun! Prussian blue is not only so blue you can't show it accurately on a computer screen - it's blue because of 'intervalence charge transfer', where the red and yellow iron atoms here trade which one has an extra electron. johncarlosbaez.wordpress.com/2025/10/03/p...

I'm trying to lose weight. I was so happy when I saw my local pastry shop sold negative-mass doughnuts. But what happened next really freaked me out. (Negative mass in Newtonian mechanics, special relativity and relativistic quantum mechanics.) www.youtube.com/watch?v=THT8...

A (purely theoretical) eternal black hole is symmetrical under time reversal, so it's also a white hole. It's quite hard to understand this picture, even if you cut out the "parallel universe". Things can pop out at any time, as well as fall in - it's time translation invariant!

In my new series of videos, Edinburgh Explorations, I'm diving into all the physics controversies I've avoided up to now. www.youtube.com/watch?v=cdiw...

If you had a negative mass star next to a positive mass star, what would it do? It would *chase after* the positive mass star, with the both accelerating toward the speed of light! A negative mass black hole is not a white hole. What is it? Fun with physics.... mathstodon.xyz/@johncarlosb...

There's no reachable position in chess with more than 218 moves for one player! Here's one with 218 moves for White. This was *not* proved by checking all 8.7 × 10⁴⁵ reachable chess positions. Instead, someone known only to me as Tobs45 figured out a better proof: lichess.org/@/Tobs40/blo...

We need an internet archive outside the US! We can't put all our eggs in one basket. Oh, wait: we *have* an internet archive outside the US. Let's support it. And now they have an office - a physical presence. flaminghydra.com/freedom-and-...

If you have a gold ring, it only exists thanks to gravitational radiation. But new paper argues it also requires neutrino oscillations! Most science journalists aren't explaining why, but I do here: mathstodon.xyz/@johncarlosb...

Go, team, go! Just when I feel we're doomed I see something that gives me hope. It's an emotional rollercoaster. But this particular rollercoaster is rolling downhill fast. Wheee! From here: ourworldindata.org/data-insight...

It's fall, the days are shrinking fast up here in Edinburgh! But it could be worse. Shortest day of the year: London: 7 hours and 50 minutes Edinburgh: 6 hours and 57 minutes Orkney: 6 hours and 10 minutes Shetland: 5 hours and 49 minutes mathstodon.xyz/@johncarlosb...

Idle speculation: if our universe had a larger number of spacetime points - a larger cardinality, a higher infinity - maybe we could do math with infinitely long statements. This would be vastly more powerful than the math we have now. mathstodon.xyz/@johncarlosb...

The United Nations has now ratified the High Seas Treaty, setting the stage to create huge conservation zones in international waters, covering 30% of the world's oceans! highseasalliance.org/2025/09/19/h...

I decided to work on quantum gravity after reading John Wheeler's wild ideas about black holes, "pregeometry" and "it from bit" near the end of his textbook Gravitation. What could possibly be more exciting? www.quantamagazine.org/john-wheeler...

Academia.edu's terms of service are pure evil. I'm seeing people say "I quit it when I got an email saying they had generated a podcast using AI based on one of my papers without my permission" and "I discovered it was sending automatically-generated emails in my name without even telling me"

ObsidianUrbex photographs abandoned places... saying "the most beautiful of all abandoned places are ones that are being reclaimed by nature. Nature is always waiting in the wings to reclaim what we have taken." mathstodon.xyz/@ObsidianUrb...

"Mirror-image biology" studies molecules that are mirror images of the usual ones. People are making mirror DNA, mirror proteins.... In 2019, the NSF gave out some grants to develop a mirror cell. Some of the researchers later decided it was a bad idea and quit. mathstodon.xyz/@johncarlosb...

I had a great conversation with Latham Boyle. We talked about our attempts to get the Standard Model from octonions. He explained some stuff about neutrino masses that I always find confusing. And we talked a bit about how black holes could form in the early universe. arxiv.org/search/?quer...

A big team of astronomers think they've found a very old black hole, 50 million times the mass of the Sun, just 700 million years after the Big Bang - and not in a galaxy. Is this unusual or typical for 'little red dots'? arxiv.org/abs/2508.21748

"All say, 'how hard it is that we have to die' - a strange complaint to come from the mouths of those who have had to live." - Mark Twain (Of course dying is part of living.)

A 'quasi-star' could form when a gas cloud over 1,000 times the Sun's mass collapses and forms a black hole. Its outer layers would be big enough to absorb the resulting supernova without being blown apart! Result: a huge star powered by a black hole. (1/2)

One statement of triality is that Spin(8) has nontrivial outer automorphisms of order 3. It's less well known that the octonions have nontrivial inner automorphisms of order 3. This is not just a coincidence, is it??? mathoverflow.net/questions/50...