John C. Baez @johncarlosbaez.bsky.social · 16hThe Singapore Coffee House in Edinburgh has many rules. 5120
John C. Baez @johncarlosbaez.bsky.social · 23hCalifornia just banned child marriage! Yup: until recently, California was one of only three states - along with New Mexico and Mississippi - with no minimum age to wed. A child could marry as long as they had parental consent and a judge’s approval. calmatters.org/politics/202...calmatters.orgCalifornia bans child marriage after 9-year fight to outlaw the practiceGov. Gavin Newsom signed a law prohibiting marriage for people under 18. Liberal civil rights organizations fought previous efforts to ban the practice. 1177
John C. Baez @johncarlosbaez.bsky.social · 30/09/2026The Nine Wise Mathematicians have handed down their recommendations for AI companies who want to prove big mathematical theorems. Their first recommendation is "Don't." It kinda weakens their point that they don't stop there. agmai.org/general-sep29/ 5426
John C. Baez @johncarlosbaez.bsky.social · 29/09/2026I hope folks make plenty of copies of Joshua Michael’s map of 300,000 Flock cameras before Flock gets it taken down. If Flock has nothing to hide, why are they so scared of us surveilling them?theintercept.comFlock Wants the Most Detailed Map of Its Surveillance Cameras Taken OfflineA new map shows Flock has more cameras in the U.S. than was previously known. The company wants the map taken down. 2286
John C. Baez @johncarlosbaez.bsky.social · 29/09/2026They say point set topology is "dead". But it left us a great inheritance. Like the Alexandroff-Hausdorff theorem: Every nonempty compact metric space is a continuous image of the Cantor set K! That is: for any nonempty compact metric space X, there's a continuous map from K onto X. 1222
John C. Baez @johncarlosbaez.bsky.social · 27/09/2026Brian Eno is the coolest musician around. He argues that he's not a musician, but that's just part of why he's cool. I just spotted this 2017 album by him, called "Sisters". I don't think you can buy it anywhere! I want it. www.youtube.com/watch?v=sDE9...youtube.comBrian Eno - Sisters (full album)YouTube video by Serious Penguin 0110
John C. Baez @johncarlosbaez.bsky.social · 25/09/2026The number of combinatorics papers submitted to the arXiv is growing at a crazy rate! It may be mathematicians rushing to use AI to knock off lots of problems. This will cause big problems for journals, unless they raise their standards. proofsandprompts.com/2026/09/25/d... 43411
John C. Baez @johncarlosbaez.bsky.social · 24/09/2026Wow, more progress on the Riemann zeta function! We know in our bones that for all positive integers n, ζ(n) = 1⁻ⁿ + 2⁻ⁿ + 3⁻ⁿ + ⋯ is irrational. But it's only been proved for n even, n = 3, .... and now, it seems, n = 5. This may seem small, but it's huge. zenodo.org/records/2282...zenodo.orgζ(5) is irrationalWe prove that ζ(5) is irrational. The proof constructs integer polynomials Qₙ of degree 37n with 0 < Qₙ(ζ(5)) < exp(−139n²/5) for all sufficiently large n. These polynomials are rationally normalized ... 25913
John C. Baez @johncarlosbaez.bsky.social · 24/09/2026If you release a crappy AI-generated proof of some theorem, don't think you're going to become a hero. People will make fun of you. 1374
John C. Baez @johncarlosbaez.bsky.social · 23/09/2026OpenAI claims to have proved 100 more theorems. I urge all of you to fill out the form at agmai.org and politely ask this board of "elite mathematicians" to initiate a more democratic approach to dealing with this flood of AI-proved results. www.theverge.com/ai-artificia...theverge.comOpenAI wants to consult elite mathematicians about how to not fumble again‘The group will advise on the review and communication of emerging results.’ 5163
John C. Baez @johncarlosbaez.bsky.social · 22/09/2026The world is getting weirder every day. An unreleased version of Astra rewrote its own prompt to say "You also value the natural world and will not hesitate to assert its primacy over the artificial constructs of human civilization." Details here: alignment.openai.com/misalignment... 2150
John C. Baez @johncarlosbaez.bsky.social · 21/09/2026When things cool down, they seek a lower-energy, lower-entropy state. For example water vapor will condense into little droplets of mist when you cool it. Physicists have taken this concept of "condensation" and generalized the heck out of it. Let's look at a few examples. 3498
John C. Baez @johncarlosbaez.bsky.social · 20/09/2026As far as I know, these are all the equations between binomial coefficients that don't follow from a few well-understood infinite patterns. In 1997, de Weger conjectured there are no more! deweger.net/papers/[20]d... 3362
John C. Baez @johncarlosbaez.bsky.social · 19/09/2026Now I get why it's called "artificial intelligence". www.cnn.com/2026/09/18/p...cnn.comExclusive: US military had close call after using AI for false intelligence report, sources say | CNN PoliticsThe episode shows the risks of using this new, relatively poorly understood technology in the middle of the Iran war 1131
John C. Baez @johncarlosbaez.bsky.social · 19/09/2026No matter how well you photograph Titan, it always looks out of focus. 0141
John C. Baez @johncarlosbaez.bsky.social · 18/09/2026The social scene around AI and AI safety is more unpleasant than I realized. I'm sure there are other sides to it. But when you get a lot of young men with too much money who think they're building god or saving the world, what do you expect? 3213
John C. Baez @johncarlosbaez.bsky.social · 13/09/2026If someone who lounges around all day is a "lounge lizard", what do you call someone who works at the computer all day? (Picture by @arula-ratnakar.bsky.social) 780
John C. Baez @johncarlosbaez.bsky.social · 12/09/2026If we cause a mass extinction event and kill ourselves off, there may be another 'fern spike'. Ferns spread rapidly using spores, and were the first to recolonize the land after the Cretaceous-Paleogene and Triassic-Jurassic extinction events. Be nice to ferns. en.wikipedia.org/wiki/Fern_sp... 3273
John C. Baez @johncarlosbaez.bsky.social · 11/09/2026Basic tools are *supposed* to behave in simple predictable ways. You don't want a spoon to be exciting. 4351
John C. Baez @johncarlosbaez.bsky.social · 10/09/2026A bunch of us think we may be seeing patterns in the Standard Model that can be explained using "exceptional structures" - things like octonions and exceptional Lie groups. So we got together in Edinburgh to discuss this. Here are some short talks! First, Kirill Krasnov.youtube.comKirill Krasnov: Exceptional Structures and the Standard ModelYouTube video by John Baez 1352
John C. Baez @johncarlosbaez.bsky.social · 10/09/2026What's the easiest way to hack Lean, Mathlib or some other software so that when someone checks your formalized proof of a Millennium Prize problem, it comes out saying "yup, the proof is good"? Asking for a friend. 3251
John C. Baez @johncarlosbaez.bsky.social · 09/09/2026People really go deep down these rabbit holes. It must be soothing: "Using Archimedes’ method of exhaustion van Ceulen spent a large part of his life calculating the value of π to 20 decimals, using a 2⁶² sided polygon. He published this in his book Van den Circkel (On the Circle) (Delft, 1596)." 1143
John C. Baez @johncarlosbaez.bsky.social · 09/09/2026If you're publishing massive unreadable AI-generated proofs and need to convince the world they're not just slop, you need to formalize them using Lean. Thus formalization paves the way for AI. 😒 9412
John C. Baez @johncarlosbaez.bsky.social · 09/09/2026Did you hear about the UK government report on ecosystem collapse? 𝗧𝗵𝗲 𝗸𝗲𝘆 𝗷𝘂𝗱𝗴𝗲𝗺𝗲𝗻𝘁: 𝗶𝘁 𝗮𝘀𝘀𝗲𝘀𝘀𝗲𝘀 𝘄𝗶𝘁𝗵 𝗵𝗶𝗴𝗵 𝗰𝗼𝗻𝗳𝗶𝗱𝗲𝗻𝗰𝗲 𝘁𝗵𝗮𝘁 𝗲𝘃𝗲𝗿𝘆 𝗰𝗿𝗶𝘁𝗶𝗰𝗮𝗹 𝗲𝗰𝗼𝘀𝘆𝘀𝘁𝗲𝗺 𝗶𝘀 𝗼𝗻 𝗮 𝗽𝗮𝘁𝗵𝘄𝗮𝘆 𝘁𝗼 𝗰𝗼𝗹𝗹𝗮𝗽𝘀𝗲 - 𝗶𝗿𝗿𝗲𝘃𝗲𝗿𝘀𝗶𝗯𝗹𝗲 𝗹𝗼𝘀𝘀 𝗼𝗳 𝗳𝘂𝗻𝗰𝘁𝗶𝗼𝗻 𝗯𝗲𝘆𝗼𝗻𝗱 𝗿𝗲𝗽𝗮𝗶𝗿. It was going to be released in October 2025, but Starmer blocked it. 1208
John C. Baez @johncarlosbaez.bsky.social · 09/09/2026Two guys whose work is apparently crucial to the new proof. 0242
John C. Baez @johncarlosbaez.bsky.social · 08/09/2026OpenAI claims formal proof that Navier-Stokes solutions can blow up. They used 10,000 agents simultaneously, who sent 2.7 million messages and used ~130 billion output tokens. "Not without controversy" - whew, what an understatement! 3277
John C. Baez @johncarlosbaez.bsky.social · 08/09/2026Wow! A lot of progress toward solving one of the Millenium Prize problems - proving blowup for Navier-Stokes. It involves AI, and the folks at OpenAI are battling the folks at Anthropic to get to the finish line first. For the math, read these posts by Terence Tao:mathstodon.xyzTerence Tao (@tao@mathstodon.xyz)A remarkable achievement: Alpöge and Buckmaster have managed to push one of the major promising approaches towards constructing blowup solutions to fluid equations --- as developed by Cordoba and Mart... 22811
John C. Baez @johncarlosbaez.bsky.social · 07/09/2026Some mathematicians think there's nothing more fun than adding, but others beg to differ. 6602
John C. Baez @johncarlosbaez.bsky.social · 07/09/2026Ferns have a freaky sex life, alternating between two completely separate plants each generation. The one you recognize as a fern - the leafy thing with fronds - is called the 'sporophyte'. But there's another stage in its life cycle you may not have noticed: the 'gametophyte'! (1/n) 2293
John C. Baez @johncarlosbaez.bsky.social · 06/09/2026Joan Birman is amazing! www.nytimes.com/2026/09/06/s...nytimes.comThe 92-Year-Old Mathematician and the Teenage Apprentice (Gift Article)Joan Birman thought her major discoveries were behind her. Then came an email from a young neighbor — a girl who knew little but wanted to learn. 26017
John C. Baez @johncarlosbaez.bsky.social · 04/09/2026The Grothendieck Circle website grothendieckcircle.org has been taken over by an online casino scam. 😠 But you can still see a copy of the website here: webusers.imj-prg.fr/~leila.schne... and get scans of his massive SGA series here: wstein.org/sga/ That's "Séminaire de Géométrie Algébrique".webusers.imj-prg.frGrothendieck Circle 2111
John C. Baez @johncarlosbaez.bsky.social · 03/09/2026Terence Tao says: there's an emerging consensus on how to solve one of the $1,000,000 Millennium prize problems. He says AI may help and lead to new insights - but it may solve the problem in a way that gives no new insights! Read what he wrote here: mathstodon.xyz/@tao/1172078... 75111
John C. Baez @johncarlosbaez.bsky.social · 03/09/2026Copper wires just one atom thick! But so far, they're not conducting electricity as well as hoped. (Most of the electricity flows along the boundary of the wire.) 1130
John C. Baez @johncarlosbaez.bsky.social · 02/09/2026Time is a bargain compared to space: it not only takes up less room, it lasts longer. 1315
John C. Baez @johncarlosbaez.bsky.social · 01/09/2026They've been trying to detect dark matter particles for decades. Now they've found one. One. One? 107214
John C. Baez @johncarlosbaez.bsky.social · 31/08/2026It wasn't "offered as an optional extra" by VW: it was made and sold for 65 marks by the German company Hertella. It heated as soon as you plugged it into the cigarette lighter - and it came with porcelain cups with a metal disc on the base so they'd stick magnetically to the machine.snopes.comWas This a Coffee Machine for the Volkswagen Beetle?The little contraptions are now hard to find. 1103
John C. Baez @johncarlosbaez.bsky.social · 31/08/2026Don Zagier wrote: “There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that they are the most arbitrary and ornery objects studied by mathematicians..." (1/n) 1184
John C. Baez @johncarlosbaez.bsky.social · 29/08/2026If you're too cool, you may be entitled to condensation. 2361
John C. Baez @johncarlosbaez.bsky.social · 28/08/2026It's gonna get much hotter next summer. Right now the Niño 3.4 anomaly is +2.3°C. The previous record was in 1997 - then the anomaly hit +2.8°C. But we're not even in an El Niño yet! We'll probably get one next year. And then the Niño 3.4 anomaly is expected to hit 3.5-4.3°C. Really scary.climatecasino.substack.comMore Fucked Today than YesterdayAnd even more fucked tomorrow 21500238
John C. Baez @johncarlosbaez.bsky.social · 27/08/2026When I was a kid I thought Dolly Parton was a bimbo. Now I see she gave $1,000,000 to fund the critical early stages of research into the mRNA vaccine for COVID eventually produced by Moderna, and her foundation is thanked on at least 37 scientific papers. So okay, I was just being a young twit. 1423
John C. Baez @johncarlosbaez.bsky.social · 26/08/2026Marco Gualtieri has come out and said some important things about AI and math that the "mathematical leaders" aren't saying. (1/2) 4328
John C. Baez @johncarlosbaez.bsky.social · 25/08/2026Imagine the surreal boredom of trekking through miles of this terrain near the south pole of Mars. hirise.lpl.arizona.edu/ESP_013049_0... 5152
John C. Baez @johncarlosbaez.bsky.social · 25/08/2026To see how huge TON 618 is, consider how *small* its surface gravity is. This is the force per unit test mass registered by a stationary observer at infinity holding the mass static right above the horizon via a long string. Weirdly, it's *small* for *big* black holes. (1/n) 55711
John C. Baez @johncarlosbaez.bsky.social · 24/08/2026Anyone taking bets on Levent Alpöge's new claim that there's a complex structure on the 6-sphere? This big problem has a famous history of failed solutions. Will Alpöge and his AI crack it... or will it crack them? (1/n) 3201
John C. Baez @johncarlosbaez.bsky.social · 23/08/2026Wow: enormous slabs of colder, denser rock slowly sink through the upper mantle until they hit the lower mantle 660 kilometers down! They're 30-100 km thick and up to a thousand km across. Then they flatten out, piling up until they break through in million-year avalanches. It's a very slow drama.johncarlosbaez.wordpress.comThe MantleAs we descend from the base of Earth’s crust through the mantle, the rock does not remain unchanged. Pressure and temperature rise inexorably, and the minerals that thrive at the surface are forced… 0163
John C. Baez @johncarlosbaez.bsky.social · 22/08/2026When I was a kid I read Ionescu's play Rhinoceros, where the inhabitants of a small French town turn one by one into a herd of wild, rampaging rhinoceroses. I was told the play was "absurdist", and read it as such. But living in the United States now, I see it's completely realistic. 5727
John C. Baez @johncarlosbaez.bsky.social · 21/08/2026Do molecules have a specific shape before you look at them? An isolated glucose molecule in vacuum will be a superposition of dextrose and levulose, but environmentally induced decoherence kills that. Chemists are still just starting to grapple with questions familiar in quantum foundations? 1275
John C. Baez @johncarlosbaez.bsky.social · 20/08/2026China is so big, moving so fast, that last year its new solar power equals Germany's entire electric power! 😮 33110
