OpenAI, the Partition Principle, and Mathematics

ComplexSystems

I can't relate to this at all. AI models will surely get better at writing "enjoyable proofs," but for now the situation is what it is. You're passionate about this problem, right? But you don't want to do the work to understand the result? Fine. There's a new generation of younger, hungry mathematicians that are highly interested in figuring out why the result is true and I am sure they'd be happy to wade through it and spoon-feed you the answer instead. Maybe they should be running things.

transitivebs

openai will take expert responses like this and improve the next set of papers it won't be long before there's no more low hanging fruit like this to complain about, and the writing / explanations of the results are superhuman as well separately, i really liked the author's denial-of-service analogy. super useful practical framing

jdw64

Is a proof that cannot be understood worthless? How would this be framed philosophically? In fact, the academic system is a kind of worldview created by humans. And as it is shared and the community grows, the problem will gradually become more complex. Because when a discipline develops sufficiently, just as in a mine where rich veins are easy to extract early on but become very hard to extract once much has been dug out... in that sense, as things gradually become more complex, once a certain threshold is reached, won't scholarship surpass the limits of human understanding? Of course, scholarship is entirely for humans, but at some point the system itself may face its limits, and then wouldn't it again reduce the existing normalized minimum within that discipline and establish a new normalization of a new logical system? In my view, perhaps for very complex work like today, AI will do it, and then there will be work that normalizes and further simplifies the results of that AI. Then, coming back to the human fold, if humans create the initial skeleton, the LLM will learn that again and it will become complex work again, and won't this create a continuing cycle? I think verification and understanding can be separated. If the proof targets a correctly formalized proposition and passes a reliable proof checker, isn't it valuable? We have obtained knowledge justified as true, but there is simply no new theory that understands that knowledge. As was the case with the Four Color Theorem... I am always curious what shape the newly compressed new discipline will take. At that time, I hope even people like me, who are intellectually behind, will be able to learn that discipline.

computerex

Wow talk about sour grapes! No one is forcing you or any other mathematician at gun point to engage with this release at all. Ridiculous drivel.

samuelknight

At first I thought this was going to be more Luddite babble, but it makes a good point. OpenAI isn't contributing if they are make unreadable papers. They should use a little more of their compute to nail interpretability. The difficulty will only get worse as AI plow deeper into the frontier and produce increasingly alien looking output. I suspect it's a workflow issue. If not, it's a bad oversight if the current generation of models are capable of making mathematical breakthroughs but can't explain how they build on existing frameworks.

flowerlad

> OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? This is a strawman. OpenAI didn't say they are expecting all mathematicians to read the solutions, incomprehensible or not. So mathematicians are upset with OpenAI for solving "their" math problems. Software engineers are even more affected by AI, yet mathematicians seem to be reacting more strongly. I don't get why.

mcshicks

"not at the Lean code, since I know very little of the actual usage of Lean, and that code was enormous" This part I don't understand. Not that anyone should read the entire Lean code of any proof, but if the statement of the theorem to be proven in lean seems to be correct, then I would think there would be at least some interest if in fact there was a formal proof (which might or might not correspond to the written proof) of something I was working on. That to me would be interesting. Or you are saying you doubt the validity of the formal proof, which would also be interesting. But saying it is of no consequence doesn't make any sense to me.

bluepeter

I've seen my entire profession vanish overnight due to AI... well, not vanish. But, yeah, software development is WAYYYY different. And I couldn't be happier. I think it's amazing. I see the productivity boost. Even if it means I can't add nearly as much value as I used to. Sorry, but I don't get why mathematicians are so upset. Like, just accept the knowledge and insights and acceleration in your field! If it isn't "fit for human consumption" because an AI produced, okay... it soon will be explained ELI5 by even better models.

heyitsdaad

Very sensible comments. It is along the lines of the fury I get when I am confronted with an 11 page dump of an issue analysis created by an AI agent that makes no sense but I have to go through because customer shared it. If you did’t bother to write it, I shouldn’t be bothered to read it. Perhaps AI agents can have their own publications and magazines where they are the chairs and associate editors and reviewers.

sigmar

>OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? Why? ... >So, no, I will not be sending Sam Altman a bottle of whisky anytime soon, nor I am planning on spending my time reading through that paper and trying to make sense of it. Think about a hypothetical circumstance where we get radio communication with some aliens on another planet. They send over tons of math to help us advance our tech, we know the math they're sending us is correct, but their explanations are really hard to work through because they aren't humans and the math is so different from anything we've done. Should we whine about the results they sent to us and refuse to engage with it?

agnishom

Very well written summary of the current situation Imagine being someone who is working on one of these problems. You have no good guarantee that the problem was solved, but you will have the horrible homework of reading the AI slop. Also, if you do have something interesting to say about the problem, people will have less enthusiasm about it now

warkdarrior

Love this! > This is why I generally avoid using AI for mathematics (I am happy to ask LLMs to consolidate information for me, or to generate a useful infographic, or to proof read an email, etc.) In other words, the author is OK with using LLMs to replace data analysts (that could consolidate information), to replace graphic designers (that could generate infographics), and to replace editors (that could proofread an email). But don't you dare use LLMs in their mathematics.

airtnp

I would admit seeing more mathematicians irritated is a good popcorn show. For what's worth it, this batch of results are not very tight intentionally by OpenAI and promising mathematicians already started to consume them and improve the results, while someone is still complaining on it.

vikramkr

This whole "oh no this problem is solved now who would ever want to work on it" thing is quite funny. Mathematicians, let me introduce you to something called bike shedding. Folks proved 1s and 0s are turing complete decades ago and yet we have 27 new JavaScript web frameworks every week (or every day or minute now with ai). Y'all will be fine. Thinking a solution is ugly and that you could do better is also a perfectly good motivator and most of the sciences and engineering are "ok, so we know xyz to be true about the world because like, I'm looking at it, but wtf is going on." The theorems were true false or otherwise before some random openai model solved them. And if you don't understand the proof nothing of significance has changed except you've got a bit of a hint now.

drivebyhooting

If he doesn’t like the paper’s structure he can just prompt gpt pro to review and amend. I know the model that produced these proofs is still private, but it’s worth a shot tackling the proofs with the current consumer-available frontier.

cs_throwaway

There is no nice way to tell someone that you’ve scooped them, and this is industrial scale scooping. A few papers have been retracted, but it looks like many are withstanding intense scrutiny. Lean is making the results more likely to be correct, but I think making them harder to understand. The world has changed and you’ll know a math department is making a serious attempt to adapt when it teaches a required Lean course in freshman year.

nxobject

In short, we’ve reinvented cranks sending unsolicited, poorly written putative proofs

adverbly

> OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? Why? I am trying to finish several papers, I am supervising a number of Ph.D. students, and I have a lot of active research of my own to do. When am I supposed to sift through a badly written paper? Why should I bother, when they don't bother to communicate better? Excellent point. I don't blame the AI for this - I blame OpenAI. Literal slop grenade (see https://fortune.com/2026/09/17/shopify-tobias-lutke-ai-slop-... )

jwilber

I see an argument about the paper being poorly written, which I believe, but I don’t see how that relates to honest final paragraph about mathematicians being chefs or whatever. It’s clear from the author’s tone about lean, emails, infographics, etc. that he thinks automating those away is fine. Why should math be any different?

pelican0

I think it can both true that 1) OpenAI is being inconsiderate/harmful/<pick-whatever-adjective> with their math releases, and 2) there is now a treasure trove of mathematical results ready for the taking. Yes, the situation sucks overall and mathematics as a whole is in a turbulent time now. But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem. #2 above is still true regardless of where it came from or how hard it can be to absorb. While reading "The Mathocalypse" post [0] by Scott Aaronson, Scott described his wife Dana's reaction to one of the newly solved results in her primary domain of expertise, on which she'd been working for decades. After her initial shock, and annoyance with the format/style, she decided to start using Astra - for the first time - to help her understand the new result. And he reported in the comments that she had made a lot of progress understanding it in one day, and may be even excited to give a talk about it! That seems like a much healthier attitude towards these new results. Yes, everything else sucks about this messy period. But there are still diamonds (in the rough) in this drop that perhaps should be looked into. If the author is too busy, perhaps one of their students can take a look? Someone will, eventually. [0] https://scottaaronson.blog/?p=10169