Well clearly not.

But it doesn't even have the resources to specify the modality, and with the truth tables they give, I don't think that's what was in mind. (This would also give the classic problem of every true mathematical theorem being necessary and sufficient for every other one).

This seems worth fixing, but I don't know the ins and outs of wikipedia editing.

Why? Because these are obviously modal notions. Extensional classical logic does not capture what they mean.

Specifically, it bases everything on material implication. But this is silly, as in classical logic you have (p->q)v(q->p), so for any two propositions, this would say one is always necessary/sufficient for the other, which is silly.

Logicians of BlueSky! Does anyone know how to overhaul a whole wikipedia article. The one for necessity and sufficiency is fundamentally wrong.

en.wikipedia.org/wiki/Necessi...

Is it a bird? Is it a plane? No, it is a substance consisting of infinite attributes, each of which expresses eternal and infinite essence.

It is wild to be doing philosophy of maths at a time where strange and new things are happening!

This week "GPT-5.4 Pro (prompted by Price)" solved Erdős problem 1196, a conjecture of Erdős, Sárközy, and Szemerédi.
www.erdosproblems.com/forum/thread...

Yeah, this is precisely a case where if a human had done it, it could be called "creative".

Philosophically, we can't say that it isn't creative because it is missing the special human magic.

(This is not to say I'm not worried about calling LLMs creative, but worried for social reasons).

Jared Duker Lichtman on X: "In my doctorate, I proved the Erdős Primitive Set Conjecture, showing that the primes themselves are maximal among all primitive sets. This problem will always be in my heart: I worked on it for 4 years (even when my mentors recommended against it!) and loved every minute of it." / X In my doctorate, I proved the Erdős Primitive Set Conjecture, showing that the primes themselves are maximal among all primitive sets. This problem will always be in my heart: I worked on it for 4 years (even when my mentors recommended against it!) and loved every minute of it.

More discussion from Jared Lichtman here: x.com/jdlichtman/s...

A fun question: is this "creativity" yet? In a way, it was just using a different technique from somewhere else in maths than experts had been using. However, it seems like it is also a proper breakthrough in the area.

The speed at which LLM-based math systems are improving is extremely rapid. The forthcoming paper I have with Silvia De Toffoli on "The Technological Turn in Mathematics" is already out of date! philsci-archive.pitt.edu/28906/

Quote from Terence Tao: "In any case, I would indeed say that this is a situation in which the AI-generated paper inadvertently highlighted a tighter connection between two areas of mathematics (in this case, the anatomy of integers and the theory of Markov processes) than had previously been made explicit in the literature (though there were hints and precursors scattered therein which one can see in retrospect). That would be a meaningful contribution to the anatomy of integers that goes well beyond the solution of this particular Erdos problem."

The interesting thing is that this wasn't "low-hanging fruit", it was something that experts had worked on and gotten partial results in. The solution was achieved by taking a different approach than previously, something that will be useful beyond the particular problem.

It is wild to be doing philosophy of maths at a time where strange and new things are happening!

This week "GPT-5.4 Pro (prompted by Price)" solved Erdős problem 1196, a conjecture of Erdős, Sárközy, and Szemerédi.
www.erdosproblems.com/forum/thread...

In memory of Barbara Jaworski. blog.lboro.ac.uk/cmc/2026/04/...

Though maybe this is the simplest explanation: "A few months after sharing his paper on Nesterov’s method, Ryu took a leave of absence from UCLA to take a job at OpenAI, where he is now a member of the technical staff."

Quote from the Quanta article reading "When Ryu asked ChatGPT, “it kept giving me incorrect proofs,” he said. “But the lead-up to the inevitable error had interesting steps, correct partial results that seemed potentially useful.” As the LLM made incremental progress, he would check its answers, keep the correct parts, and feed them back into the model with a new prompt. “I had to play the role of the verifier,” Ryu said. “With ChatGPT, I felt like I was covering a lot of ground very rapidly, much more quickly than I could do on my own. That’s what kept me going.”"

Hi Dave! Yeah, nice question. This quote was surprising to me, for example, because I had thought that being a reverse centaur was not something anyone wants to be, but they seem to be delighted.

Lots of nice details about the latest maths, which is good, but basically no dissenting voices which is bad. A lot of this reads like it was written by the PR departments of the tech companies the mathematicians are working for.

Journalist writing about math speak to at least one woman challenge: impossible.

The AI Revolution in Math Has Arrived | Quanta Magazine AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.

A big new Quanta write-up of the current state of AI in maths.

www.quantamagazine.org/the-ai-revol...

Seems a bit contrived to make ships spar with the pope before eliminating them.

And as I'm making my round in the supermarket, I see that <someone is making a mess>, bad philosophy papers strewn across the floor.
I follow the trail of bad philosophy papers, I end up in the same place as I started, even more of a mess on the floor now.
I realise <I am making a mess>.

A thread🧵about formalisation and the abc conjecture.

A new Mochizuki paper was just posted! This one is unusually interesting, as it is about formalisation efforts for the abc conjecture "proof".
www.kurims.kyoto-u.ac.jp/~motizuki/Fo...

The other paper is in Topoi on "Inferentialism meets Feminist Logic":

rdcu.be/fcXUj

I argue (very roughly summarized) that inferentialism can be informed by an approach of feminist logic in an interesting way 😊

A comic collaboration with Terence Tao. (How does he find the time???)

www.smbc-comics.com/comic/sphere...

look I support NSF but I don’t think they should have been funding a decades-long chimpanzee civil war

Strong agree. My most cited paper has a lot of extra machinery that is not so important to central point it makes. It would be pretty unhelpful for most people wanting that point to wade through the technicalities.

Overall, I'm interested to see what happens. Assuming the abc "proof" isn't right, my bet would be that they get stuck somewhere and the project fizzles out. For the sceptical maths community, this would probably be taken as a sign that Scholze and Stix were right all along.

Spaghetti code would certainly be antithetical to the "clear structure and communication" goals mentioned above.