John Baez
Mathematical physicist at UC Riverside. Wrote This Week's Finds in Mathematical Physics and now the Azimuth blog on mathematics, physics and environmental science.
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Latest Mastodon
- This article says the implications of the newly proved quasi-Riemann hypothesis are "staggering" - but it doesn't mention any. So what are they? First, remember the number of primes less than n is roughly n / ln(n). The Riemann hypothesis lets us make this more precise. So does the quasi-Riemann hypothesis, though it's not as good. Let's get into it! For all this it's better to use, not n / ln(n), but a more precise estimate of the number of primes less than n: a function called li(n), which is the integral of 1/ln(x) from 0 to n. The difference between this and n / ln(n) is a lot bigger than… quantamagazine.org
Recommends rcmnd
rcmnd What they recommend 10 things — each backed by an exact quote.
Compiled by rcmnd.app, not by them: the quotes are theirs, and each links to the post it was copied from.
Recent
Uses Instiki
This uses some software called Instiki, but another guy takes care of that, a whiz named Andrew Stacey - not me.
usesthis.com 25 Jul 2013
Uses WolframTones
I've been recording electronic music using strange software like WolframTones, which lets you 'evolve' pieces using cellular automata, or QuasiMusic which generates sounds mathematically from quasicrystals - patterns that almost repeat but never quite do.
usesthis.com 25 Jul 2013
Uses Yamaha Clavinova
But I also like improvising in more traditional ways. I play an electronic piano, a Yamaha Clavinova, and also drums: a dumbek and a couple of frame drums.
usesthis.com 25 Jul 2013
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Uses Audacity
I do a lot of sound editing using a free program called Audacity.
usesthis.com 25 Jul 2013
Uses IrfanView
I spend a lot of time writing papers and preparing talks with free software: emacs for text editing, LaTeX for typesetting, and IrfanView for editing images.
usesthis.com 25 Jul 2013
Uses emacs
I spend a lot of time writing papers and preparing talks with free software: emacs for text editing, LaTeX for typesetting, and IrfanView for editing images.
usesthis.com 25 Jul 2013
Read The Silk Road: A New History
The Silk Road: A New History by Valerie Hansen. I'm going to western China this summer for a math conference, and then we'll go to Dunhuang, an old city on the Silk Road with hundreds of caves full of paintings.
usesthis.com 25 Jul 2013
Read Principles of Planetary Climate
Principles of Planetary Climate by Ray Pierrehumbert. This is one I'd like to read, which I've bought, but haven't gotten far into. It tackles climate physics, not just on Earth but other planets.
usesthis.com 25 Jul 2013
Loved The Higher Infinite
The Higher Infinite by Akihiro Kanimori. This book is about the whoppingly big infinities that logicians invent. I used to dislike this stuff, because it seemed useless. Now it's just a hobby for me, to stretch my mind.
usesthis.com 25 Jul 2013
Loved Control System Design
Control System Design by Bernard Friedland. Control theory rocks! I've been meaning to learn it for years. The math is easy, but the idea of setting up feedback loops to stabilize systems is cool, and the techniques to do it optimally are really fun.
usesthis.com 25 Jul 2013
Where they publish
Site math.ucr.edu/home/baez His long-running academic home page: papers, This Week's Finds, course notes.
Link verified 5 Sept 2026.
Blog Azimuth His blog on mathematics, physics and environmental issues.
Open johncarlosbaez.wordpress.com
Link verified 5 Sept 2026.
Mastodon @johncarlosbaez@mathstodon.xyz His Mastodon account, where he posts daily mathematics.
Recent
- This article says the implications of the newly proved quasi-Riemann hypothesis are "staggering" - but it doesn't mention any. So what are they? First, remember the number of primes less than n is roughly n / ln(n). The Riemann hypothesis lets us make this more precise. So does the quasi-Riemann hypothesis, though it's not as good. Let's get into it! For all this it's better to use, not n / ln(n), but a more precise estimate of the number of primes less than n: a function called li(n), which is the integral of 1/ln(x) from 0 to n. The difference between this and n / ln(n) is a lot bigger than… 20 Oct 2026 quantamagazine.org
- OpenAI, Anthropic and the Simons Institute have promised to contribute enough money to pay a typical US math postdoc to work for 2 months on each of the 719 papers OpenAI recently released: $15,000,000/(719 × $125,000) ≈ 1/6 where $125,000 is typical annual salary + benefits + overhead. 19 Oct 2026
- Has anyone thought about this nonassociative deformation of the exterior algebra on two generators? I came up with it while thinking about particle physics. What I like about it is that SL(2) acts as automorphisms for every value of the deformation parameter t, and when t = 1 there's a nontrivial square root of 1. I'll give a lowbrow and a highbrow description. LOWBROW. It has elements a+bJ+cK+dL obeying J² = t K² = L² = 0 JK = -KJ = tK JL = -LJ = tL KL = -LK = t + (1 − t)J where t is a parameter in our field. When t = 0 it's the exterior algebra on two variables K and L, so J = KL has J² = 0… 19 Oct 2026
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- RE: https://social.anoxinon.de/@ninawillburger/117460862393689978 An everyday item becomes impressive if it has survived over 5000 years in a bog. 18 Oct 2026
- It's Hamilton's Day! For a long time Hamilton was trying to invent a 3-dimensional number system where he could add, subtract, multiply and divide. Finally, on the 16th of October, 1843, he realized that he needed a 4-dimensional number system - now called the quaternions. While walking with his wife along the Royal Canal to a meeting of the Royal Irish Academy in Dublin, he made his momentous discovery: "That is to say, I then and there felt the galvanic circuit of thought close; and the sparks which fell from it were the fundamental equations between 𝑖, 𝑗, 𝑘; exactly such as I have used… 16 Oct 2026
- Yesterday I went to the University of Glasgow to speak at their physics colloquium. Afterward my host took me to the Hunterian Museum. This has a big exhibit on Kelvin's electromechanical gadgets - but also one on the Antonine wall. I hadn't heard of that wall! 160 kilometers north of Hadrian's more famous wall, it stretches 60 kilometers from a bit north of Glasgow to a spot on the Firth of Forth west of Edinburgh. Unlike Hadrian's wall, it's not made of stone, so there's not so much to see. It was made of turf on a stone foundation, sometimes with a wide ditch on the north side. The Romans… 15 Oct 2026
- RE: https://mastodon.social/@mcc/117436268385215562 This tale - it's long, read it! - reminds me why I try to minimize my time programming. I'm not sure why math seems so much easier to me, but one reason is that I don't like to remember precise syntax: I don't like it when the world blows up if I forget a comma or something. 15 Oct 2026
- In this interview Strogatz manages to reinforce plenty of the worst cliches about mathematicians: they're all men, Erdős was completely unable to live a normal life and popped amphetamines all the time, Perelman never cut his fingernails, etc. He analogizes the pleasure of solving math problems to masturbation. And the strange part: he seems to think this is all most charming. It's part of his explanation of how human mathematics is worth supporting. It might have the opposite effect. (Hmm, but so far people commenting on the New York Times loved what he said - not this stuff, the other stuff… 13 Oct 2026 nytimes.com
- RE: https://backend.newsmast.org/@ToposInstitute/117429134130990740 This is one of my favorite places for research in the UK. I visited it last week and talked to Tim Hosgood about this project on ecological modeling using category theory. If you get this job, I'll be wanting to help you out... because this has been a long-term dream of mine: category theory to save the planet. 12 Oct 2026
- We may finally know that for any n, there exist n² unit vectors in ℂⁿ that all lie at the same angle from each other! This is important in quantum physics, but also geometrically very pretty. Zauner conjectured this was true in 1999. Last year Appleby, Flammia and Kopp showed it would follow from two conjectures in number theory. On September 29th, Radchenko and Wheeler put the proof of one of these conjectures on the arXiv. Interestingly, it makes use of some serious category theory - as well as shitloads of Galois theory, quantum dilogarithms, and more! But what about the *other* conjecture… 11 Oct 2026
- As threatened, OpenAI dropped a shitload of math papers. 722 to be precise: https://github.com/openai/math/blob/main/overview.pdf None solve Millennium Prize Problems or other ultra-famous conjectures. Paper number 312 proves a version of the Homotopy Hypothesis, one of my favorite math problems. I guess I was the first to call it the homotopy hypothesis. It says homotopy types are "the same" as "infinity-groupoids". Depending on how you make the quoted phrases precise, this hypothesis comes in many versions: some easy, some hard. None of the OpenAI papers will affect my work. 7 Oct 2026
- A theorem you'll never forget: Napoleon's theorem. Take any triangle. Erect equilateral triangles on its three sides. The centers of these triangles are the vertices of another equilateral triangle! While traditionally attributed to Napoleon, who *was* interested in geometry, there's no good evidence that he proved it. In reality, this result first appears in 𝘛𝘩𝘦 𝘓𝘢𝘥𝘪𝘦𝘴' 𝐷𝑖𝑎𝑟𝑦 in 1824, posed as a puzzle by one "Mr. W. Rutherford of Woodburn". This guy is famous for having computed pi to 208 digits... of which only the first 152 were correct. The proof here claims to be "geometri… 4 Oct 2026
- I've been thinking about life after the ecological collapse. Many of the species we love will be extinct. But probably not liverworts. Liverworts were among the first plants to bounce back after the world-wide rain of molten quartz set all the forests on fire when an asteroid hit the Earth 65 million years ago. They were among the first to bounce back after the much worse end-Permian extinction. They've been around for 420 million years, but with bursts of new species beginning in the mid-Jurassic and continuing through the Cenozoic. Liverworts are so deeply evolved that when you search the i… 3 Oct 2026
- I don't take drugs, but I do sometimes listen to Helado Negro's psychedelic neo-tropicalia. For me the most catchy of his productions is "Invisible Hearbeat". It has a big bouncy bass and drum, almost verging on aggressive, but never getting there - and his voice floats over it so smoothly it's clear there's no danger here, except of getting lost in the swirls and curls of sound. Tú no sabes más con mi Hablas más Tenemos todo (todo) aquí Tenemos todo (todo) fácil Y bailas, bailas, bailas Uh Sola, sola, sola Ah Bailas, bailas, bailas Uh Sola, sola, sola Ah (1/n) 2 Oct 2026 youtu.be
- Martin Schwartz wrote an article called "The importance of stupidity in scientific research": https://fermatslibrary.com/s/the-importance-of-stupidity-in-scientific-research I agree with most of it, but I think what he calls stupidity should really not be called stupidity: he means "admitting our ignorance". For example, he writes: "Second, we don’t do a good enough job of teaching our students how to be productively stupid – that is, if we don’t feel stupid it means we’re not really trying. I’m not talking about ‘relative stupidity’, in which the other students in the class actually read the… 2 Oct 2026
- Patrick Fitzsimmons argues that big Bronze Age states collapsed around 1200 BC when people figured out how to smelt iron instead of relying on a few far-flung tin mines to make bronze, thus democratizing weapons manufacture. I don't know, but the quotes here are pretty cool: "The effects of iron were so stark that ancient writers in the subsequent centuries began separating human history into the bronze and iron eras. Hesiod described the age of iron as a time of suffering and strife, where no man knew a day or night free of toil or pain. Herodotus writes in his Histories that working iron wa… 30 Sept 2026 worksinprogress.news
- The 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. 30 Sept 2026 agmai.org
- I hope folks make lots of copies of this map of 300,000 Flock cameras before Flock gets it taken down. 28 Sept 2026 theintercept.com
- I went to Glasgow to give a talk on the 4d rotational symmetry of the hydrogen atom, but what sticks in my mind is the beauty of ferns, tree ferns, mosses, liverworts and other "primitive" plants on display at the Glasgow botanical garden! (1/2) 28 Sept 2026
- RE: https://mathstodon.xyz/@highergeometer/117323453342622319 Wow, 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. 24 Sept 2026
Link verified 5 Sept 2026. Recent items update automatically from the channel.
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