Thomas Bloom

@AcerFur @teortaxesTex I think so yes (but there is probably also interest showing the other more inclusive graphs as well)

@thomasfbloom @teortaxesTex To be clear, I assume we both agree that the AI solution count should be only those marked as full solutions in the 1(a) category?

Over 10 solved (and many more still pending assessment!) in less than two weeks is some insanely rapid progress...

@AcerFur @teortaxesTex I think the clean/honest way is to post a graph of just AI solutions, but always with the note "currently AI solutions are 30 out of the 540 solutions known" (with whatever correct numbers)

@AcerFur @teortaxesTex Trouble is that human solutions are harder to track honestly; partially why I never tried to 'date' solutions. (When a comment was posted? The arxiv? Journal version?)

@AcerFur @teortaxesTex It would be better to generate a graph from the data at github.com/teorth/erdospr…, which does correspond to actual new AI solutions and has dates etc. Presumably it would be quick to code up something that generates this, which is what people here are generally interested in

@thomasfbloom @teortaxesTex Right indeed sorry I should have elaborated on that point, but didn’t feel the need to here since the value is actually going up from new problems being solved at the moment. I will ensure to mention this in future though

@AcerFur @teortaxesTex So the 'solved' graph is not actually tracking 'new problems being solved' (but the data in the last few weeks does correspond to this)

@AcerFur @teortaxesTex Correct. Also the 'solved' count goes up when an old solution is discovered in the literature, or when a new problem is added to the database already solved.

I hope that, in all of the publicity around recent AI solutions of Erdos problems, at least a few people have actually read the maths and learned some of the theory behind e.g. primitive sets. The role of these problems as AI headlines is secondary to some beautiful mathematics!

@wtgowers @peritutvivat Absolutely. On the other side, when writing for an expert it seems to struggle identifying which parts of its proof are 'new', spending pages rederiving classical results known for a 100 years, and then briefly sketching the actual new insight.

@thomasfbloom @peritutvivat This kind of mathematical empathy does seem to be a weakness of LLMs for the moment. If I pretend to be a weak student and ask for an explanation of some maths, I get responses that weak students would obviously find confusing and unenlightening.

It's interesting to note the language that comes up very frequently in AI-written mathematical proofs/papers, and yet hardly ever in human writing. For example, AI always wants to talk about the 'architecture' of a proof. It's also very fond of giving catchy names to each step.

@davikrehalt @AcerFur @littmath Definitely, the arxiv system (and journals in general) will have to become a lot more discerning.

@thomasfbloom @AcerFur @littmath Plus I think it would overwhelm the arXiv system soon if capabilities are increasing and everyone does this.

FWIW I fully expect what’s happening with Erdős problems to happen to other areas too, likely within the next year or so. When I say this hasn’t happened yet, that’s all that I mean!

@davikrehalt @AcerFur @littmath Definitely! This will end up being a vast repository of maths which will, almost entirely, never be read by human eye but only by AI/search engine. (This is still valuable of course, as you say.)

@thomasfbloom @AcerFur @littmath There can be a lot of value of such things right? Like if we have a large collection of things which are nontrivially true but not of huge value of themselves--then some point it can be a useful input to some other proof of things people do care more about if it's easily searched

@radokirov @littmath 'Prestige arbitrage' is a very useful phrase to describe something I've been thinking about a lot recently - thanks!

Exactly, as Tao said we are in a mode of proof abundance (and no sign that this would somehow stay limited to erdos problems). The casual observer hasn’t realized that so there is an “prestige arbitrage” opportunity - someone just asked ChatGPT and someone else is impressed by that because they have not updated their thinking that proofs are abundant now. What will happen at some point is no one will be impressed, which means people who were in it to exploit the prestige gap will leave, and hopefully more math experts will adopt these tools and we will have the real conversation of how to focus on “proof digestion” (Tao’s concept)

@monoxxxx I wrote a blog post choosing my personal 'top 10' of the most interesting/difficult Erdős problems, which you might be interested in. erdosproblems.com/forum/thread/b…

エルデシュ未解決問題集は「未解決問題」というシンボリックな呼称がゆえ解けたときの話題こそあれど、それぞれの難易度差は(解かれた結果論的には)歴然なので(某廻戦で宿儺とそれ以外の特級が同じ特級呼ばわりされてるのとイメージは近い)、過小評価は良くないが同時に過大評価もよくない

@AcerFur @littmath But otherwise, the problem is that so much writing is now being generated, hardly any of which is actually being read (including by the people who asked the question of AI in the first place!) So what is the point in it existing, or being stored, if it is never read?

@AcerFur @littmath I can see a future where there is some central repository, an 'AI-arxiv', where people can post such solutions, and then if and when another human in the future is curious they can search, and see 'aha yes, this question about additive bases was solved by GPT-5.5 in 2026'

@littmath A 'Litt-mus Test'?

@thomasfbloom I’ve been thinking about starting “Problems-I-Like-Bench.”

@AcerFur @littmath And then a formal paper/publication should be reserved for when an AI insight has been properly digested by humans, who can explain it in its proper context and apply it to genuinely important problems (e.g. the recent primitive sets paper).

@AcerFur @littmath Indeed - but most of the AI solutions don't need to be full papers! There will need to be a better way of hosting such AI-generated answers, that can store any insights people have obtained for others to peruse, to save others from re-asking their own AIs.

@peritutvivat Human experts know what is new, and which things to focus on in an exposition of a proof; they can anticipate which parts of a proof another human actually needs explaining.

@peritutvivat This is less about that specific language, but a major problem with AI mathematical writing (at the moment) is that it tends to give all steps equal weight - everything is a key step, everything seems equally hard and important.

@littmath Unless of course someone sets up a website full of open problems in algebraic geometry in an easy copy-able format...

@littmath I agree, but I'm not sure if the general public will hear much about it when that happens. There will also be much less of the 'amateur solved open problem in an AI one-shot', because they simply won't be interested in the answer!