lhd1

I have no issue taking arbitrary derivatives... provided you're not taking derivatives of very noisy data.

Is this a major concern? I can imagine them selling the excess compute to other LLM providers just as SpaceX did with Anthropic.

Whether you think they have a future or not does not change fact that they currently are wildly unprofitable.

>internet thing wasn’t going anywhere.

This is conflating the utility of the technology with the economics behind it. Few people claim LLMs are useless. It's a question of figuring out a viable business model.

It would help if this was also written up in the conventional way as a scientific paper (Intro, methods, conclusions, etc). These discursive blog posts are getting exhausting.

Are you suggesting that Tao, whose banner image on his blog is a quote from On Proof and Progress, has not read Thurston's essay?

it's a lot of style over substance

I wonder - was there really no other people they could have given it to? The detection of gravitational waves was split between a theorist, experimentalist and a person who had a big hand in shepherding the project along. Could not the same have been done here?

there are so many extraordinary things about von Neumann that there seems little need to write a fictionalized account of his life. How is the reader to know what is real and what is fiction?

several authors including the creator of arxiv, Paul Ginsparg, foretell a future in which we "increasingly rely on status markers such as author pedigree and institutional affiliation as signals of quality, ironically counteracting the democratizing effects of LLMs on scientific production." I think this is a very plausible outcome of a flood of preprints. Because there's only so much time in a day and are we going to spend it on papers by less established people who we do not trust? It's a pity. If the science is good what does it matter who produced it.

https://arxiv.org/abs/2601.13187

Much of Susskind's papers are like that. A few simple equations motivated by dimensional analysis, a couple of Penrose diagrams, and the rest speculation and insight.

lo and behold, a 1000 word sample comes back in Pangram as AI generated. This should not be worth anyone's time (and maybe you have spent more time on your comment than the author did in their blogpost).

>Mathematics is probably the same way. There's a short-term rush when you pull the lever, but there's less desire to get invested in what comes out.

Perhaps it will take until the next generation to come along to really embrace the new AI-assisted way of doing mathematics. The current generation has too many reservations.

If you consider this event in isolation it is cause for celebration. But the controversy around this isn't so much about how the proof was obtained but what this means for the practice of mathematics going forward. It seems we can probably expect more and more results of this nature being dumped into the community. It's happened before that one person, Bill Thurston, was so successful in his field, proving theorem after theorem, that he inadvertently killed his field. People hesitated to enter his field, knowing that they could be scooped at any moment. It took years before his field recovered - and I think his famous essay was written in response to this.

https://arxiv.org/abs/math/9404236

It would be good if someone made a list of allresults obtained with AI so far just to see what kinds of problems AI excels at. Are there any that aren't of the existence-proof type?

Reductively, math can be said to be either problem solving or theory building - it seems the latter is a much harder thing to do right now.

This is also what I've been thinking. The result itself is amazing but it's not like this was completely unexpected. There has been a huge amount of progress on the problem in the last 10 years without which it seems unlikely today's full resolution would have been possible. It is not clear what strategy was taken but it sounds like it borrowed heavily from the two spanish mathematicians. Experts will scrutinize the proof and it will be interesting to see if anything truly original or unexpected was done, outside of known techniques, a move 37.

So what do you think his contribution was? His preprint record shows no research on fluids - and the statement says that the first LLM-generated proof Tristan received from Levent was 'the most horrendous I have ever read.' Levent is out for mathematical scalps whether it is in his field of expertise or not, and he has the resources to do it. And I am not saying he is not a very clever person, but the idea that you can bring yourself up to the forefront of research in PDEs, in particular NS, and contribute new ideas in less than a year is implausible.

I find the framing a little strange, a sort of David vs Goliath (with his enormous computational resources at his disposal). Since Levent is at Anthropic whose internal models are presumably as capable as anything OpenAI has. So why wasn't Anthropic behind their effort? Why did Tristan use OpenAI's models when it should have been known was a potential outcome? I understand they wanted a normal math collaboration but presumably what Levent brought was his resources (as far as I can see Navier-Stokes is not his speciality). Normally these things are hashed out formally beforehand to avoid the sort of thing now happening.

This point of view is essentially codified in effective field theory, which tells us why so much of classical physics (EM, fluids, gravity) can be seen as low order approximations of some more complete theory that we found later on. One of the great insights from 20th century physics imo.

and you can do one better than that - Birkhoff's theorem, the relativistic analogue of the shell theorem.

https://en.wikipedia.org/wiki/Birkhoff%27s_theorem_(relativi...

One of the cool facts about gravity is that the gravitational field of a body 'feels' spherical at a distance, even if those bodies are not spherical themselves. There are higher multipoles but they are increasingly suppressed the further you are from the body. So at least for gravity the spherical approximation turns out to be good and justified.

Incidentally, Duminil-Copin, who also works in percolation theory, wrote an essay on the impact of AI on math.

https://proofsandprompts.com/2026/08/30/care-for-a-little-mo...

Scott Aaronson spoke about this in a colloquium where he said that this was mooted at OpenAI before the decision was made by Altman to not implement it for the reasons you describe.

https://youtu.be/9udWn1Hlj_s?si=VWOiK5-y4zcyDoHI

can we have a moratorium on notetaking apps?

they are friends according to https://www.ams.org/journals/notices/202607/noti3372/noti337...

Look for triads and "it's not this, but that". These are dead giveaways. You can also pass it through Pangram which is quite reliable these days.

find it difficult to engage with AI generated text. What am I getting here that I couldn't get from a chatbot.

I was expecting Grothendieck. Conway is hardly the poster child for theory building.