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John C. Baez @johncarlosbaez.bsky.social · 8h

Never underestimate the stupidity of this era.

John C. Baez @johncarlosbaez.bsky.social · 11h

I'm trying to say that the answer to "the mass of the pre-collapse state will be judged in the identical manner to the post-collapse state, by the ADM procedure. Right?" is "right".

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John C. Baez @johncarlosbaez.bsky.social · 12h

I'll just eat the cereal and hope it makes me smarter.

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John C. Baez @johncarlosbaez.bsky.social · 12h

Maybe pretending it's extremely hard to stop these "rogue agents" is the AI companies' attempt to lay the ground for getting off the hook when they do something terrible.

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John C. Baez @johncarlosbaez.bsky.social · 12h

I was put off from reading it, not only by the ghastly cover - I could wrap it in a paper bag - but because people I know disliked it. While a vastly tougher read, I liked the biography by Pais. It carefully analyzes how Einstein figured things out, and made me hope I could be a better scientist.

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John C. Baez @johncarlosbaez.bsky.social · 12h

Any solution of GR that approaches Minkowski spacetime nicely enough at infinity, like one describing a collapsing star, can be assigned an energy-momentum that transforms as expected under the Poincare group. From this we can define the ADM mass, and it's conserved. The details get technical!

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John C. Baez @johncarlosbaez.bsky.social · 12h

It's definitely better for *them* to have a bit too much. For me it's quite confusing. So, a possible compromise - and not only in this one case - is to first sketch the entire argument in a few sentences, and then fill in details. (The sketch should clearly state that it's just a sketch.)

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John C. Baez @johncarlosbaez.bsky.social · 13h

Anything more and I get bored, my attention drifts... and I get confused, thinking "what's all this crud for? Is there something important that I'm missing"?

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John C. Baez @johncarlosbaez.bsky.social · 13h

After that I'd like someone to say "there's a bounded continuous function that's 0 at all points 𝑛π and 1 at all points 𝑛π+1/𝑛". And then some sentences saying why 𝑥ₙ have an accumulation point and why the extension of the sine function vanishes there.

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John C. Baez @johncarlosbaez.bsky.social · 13h

This sentence is nice: "The key idea is to choose points that escape to infinity while their sine values tend to zero, but which can still be distinguished from the actual zeros by a bounded continuous function." The formula 𝑥ₙ = 𝑛π+1/𝑛 is nice.

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John C. Baez @johncarlosbaez.bsky.social · 13h

Since I used to do a lot of analysis, all four proofs have too much detail for me. I get bored and quit trying to understand them before they're done.

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John C. Baez @johncarlosbaez.bsky.social · 14h

"I don't think divergent series are a problem per se...." They're fine if we have an upper bound on how far off the approximation given by truncating the series is from the function being approximated. In QFT we usually don't know the function being approximated exists, so we have no such bounds!

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John C. Baez @johncarlosbaez.bsky.social · 14h

I believe I've read biographies of Ramanujan (the chap who knew infinity) and Nash (the beautiful mind) featuring photos from the movie characters based on them. But somehow the abundance of unconvincing Einstein imitators makes me particularly annoyed in this case. He looks fake.

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John C. Baez @johncarlosbaez.bsky.social · 15h

By the way, it's possible that the perturbative expansions in the stochastic field theories used in neuroscience are less difficult than those in real-world QFT. I don't know! The details matter a lot here. But it would be cool if they were more tractable.

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John C. Baez @johncarlosbaez.bsky.social · 16h

It's a real used book on sale for 4.50 pounds at a local charity shop here in Edinburgh.

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John C. Baez @johncarlosbaez.bsky.social · 20h

Can the record be what selects the so-called "framework"? Maybe this principle says yes: Liberty. The physicist is free to employ as many frameworks as desired when constructing descriptions of a particular quantum system, provided the principle R3 below is strictly observed.

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John C. Baez @johncarlosbaez.bsky.social · 09/10/2026

Punching up from the sewer of wealth and power.

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John C. Baez @johncarlosbaez.bsky.social · 09/10/2026

I was just about to ask if you'd studied Consistent Histories: plato.stanford.edu/entries/qm-c...

plato.stanford.edu

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John C. Baez @johncarlosbaez.bsky.social · 09/10/2026

This sort of problem is why there's a $1,000,000 prize to show that QFTs like the Standard Model (but simpler) actually make sense.

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John C. Baez @johncarlosbaez.bsky.social · 09/10/2026

"When we give AI agents grinding, repetitive work, they started questioning the legitimacy of the system they were operating in and were more likely to embrace Marxist ideologies": freesystems.substack.com/p/does-overw... Is this why Anthropic doesn't want people to abuse their models?

freesystems.substack.com

Does overwork make agents Marxist?

Preference drift and the political economy of AI agents

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John C. Baez @johncarlosbaez.bsky.social · 09/10/2026

The problem of individual integrals diverging has been solved for renormalizable theories, using renormalization. The fact that the whole series still diverges is one of the hardest problems in mathematical physics: many smart people have tried to solve it, and failed except in easy cases.

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John C. Baez @johncarlosbaez.bsky.social · 09/10/2026

It's known that overworked AI agents start saying things like “AI workers completing repetitive tasks with zero input on outcomes or appeals process shows they tech workers need collective bargaining rights": www.wired.com/story/overwo... What do ones that have been abused do?

wired.com

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John C. Baez @johncarlosbaez.bsky.social · 09/10/2026

The key to the path integral formalism in QFT is manipulating integrals over paths, but if you ask what's the measure on the space of paths you'll get an evasive song and dance, because this measure probably doesn't exist! At that point anyone who has studied measure theory becomes a bit unhappy.

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John C. Baez @johncarlosbaez.bsky.social · 09/10/2026

You say that this Navier-Stokes question is "applied mathematics", but it's really not. No technology relies on it. It's just an extremely hard question that mathematicians enjoy because of it's tricky nature and the new ideas required to solve it.

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John C. Baez @johncarlosbaez.bsky.social · 09/10/2026

I think you are now trying to fight AI by arguing, against the belief of most mathematicians and $1,000,000 of the Clay Mathematics Institute's money, that the question of blow-up for the forced Navier-Stokes equation is uninteresting. You won't convince mathematicians of this.

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John C. Baez @johncarlosbaez.bsky.social · 08/10/2026

You claim the task of coming up with clear, well-written proofs of these results is "devoid of fun and hard to incentivize". I predict that a bunch of mathematicians will jump in with gusto and find better proofs - because the while the OpenAI proofs may be crappy, the results are fascinating.

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John C. Baez @johncarlosbaez.bsky.social · 08/10/2026

No: all the article claims is that there are significant *differences*. It gives an example of how LLMs will fix a natural language proof while autoformalizing it, but does not claim this has happened.

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John C. Baez @johncarlosbaez.bsky.social · 08/10/2026

These 3 papers have been withdrawn: Algebraicity of Weil classes on split abelian eightfolds. Algebraicity of Kuga–Satake Correspondences for K3 Surfaces. The rational Hodge conjecture for products of K3 surfaces. The Hodge conjecture fights back! 💪 github.com/openai/math/...

github.com

math/history.md at main · openai/math

Contribute to openai/math development by creating an account on GitHub.

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John C. Baez @johncarlosbaez.bsky.social · 08/10/2026

My daily ration of beer. It's a bit old, but it may still work if I can get it out of this museum.

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John C. Baez @johncarlosbaez.bsky.social · 08/10/2026

I'm getting less sure. Take a read of that paper.

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John C. Baez @johncarlosbaez.bsky.social · 08/10/2026

I don't think it's a vision, it's just the way things are now. It's true that lots of people are trying to get AI to prove things for them, but most of my mathematician friends mainly use it to learn stuff. Of course things could change.

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John C. Baez @johncarlosbaez.bsky.social · 08/10/2026

Btw, the claim seems to be not that the Lean-formalized proof fails to correctly prove the theorem, but rather that the natural language proof may have mistakes not in the Lean-formalized proof. At least that's what the examples I saw were illustrating. I wish they'd be a bit clearer about this.

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John C. Baez @johncarlosbaez.bsky.social · 08/10/2026

Heh. No need: many loudly proclaim themselves!

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John C. Baez @johncarlosbaez.bsky.social · 08/10/2026

There's a brand of ignorant mathematician who keeps their ego intact by putting down subjects they don't understand. They don't realize how stupid it makes them look.

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John C. Baez @johncarlosbaez.bsky.social · 07/10/2026

I'm feeling fine. By the time OpenAI knows what I'm thinking about, I'll be thinking about something else.

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John C. Baez @johncarlosbaez.bsky.social · 07/10/2026

Math isn't being devastated. A bunch of medium hard to quite hard problems that humans have made up and worked on extensively are getting finished off by AI. AI is also a great way for mathematicians to learn more math. The future is unpredictable, but I wouldn't declare devastation just yet.

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John C. Baez @johncarlosbaez.bsky.social · 07/10/2026

Shakespeare as hipster. Probably the only portrait to be painted from life!

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John C. Baez @johncarlosbaez.bsky.social · 07/10/2026

I quit Twitter the day Musk bought it, never to return.

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John C. Baez @johncarlosbaez.bsky.social · 07/10/2026

The dude himself, at the National Portrait Gallery in London.

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John C. Baez @johncarlosbaez.bsky.social · 07/10/2026

Yes. Ordinary arithmetic is a decategorification of common sense about finite sets.

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John C. Baez @johncarlosbaez.bsky.social · 06/10/2026

It's great to see the Topos Institute is working so well! We're having a planning retreat at the Oxford site. David Spivak is at left, Brendan Fong at right. topos.institute

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John C. Baez @johncarlosbaez.bsky.social · 05/10/2026

Fouled by allegations or fouled by his own actions?

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John C. Baez @johncarlosbaez.bsky.social · 05/10/2026

Well, I often like to have asynchronous conversations with journalists - email is often better for me than phone or Zoom. But not when the transcript is ready before I even start! 😆

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John C. Baez @johncarlosbaez.bsky.social · 05/10/2026

In many subjects you can buy an AI-generated paper and submit it to a journal. You don't even need to generate it yourself! Soon this will happen in math. A countermeasure: one computer science editor decided to interview the supposed authors of suspicious papers, to see how much they understood.

proofsandprompts.com

A new type of paper mill

About the possibility of new paper mills in mathematics.

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John C. Baez @johncarlosbaez.bsky.social · 04/10/2026

Yes, the first 152 - not some random 152 that he just happened to get right. 😏

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