Comment by XorNot
11 hours ago
That seems short sighted though. A few years ago models couldn't do this at all, I'm not sure there's any evidence to suggest exploring and refining results is outside their capabilities or will remain so.
OAI obviously have a fiscal incentive here, but to presume a year from now we won't see improvements and more succinct work on the results coming from models?
The problem is that one a person writes a 60 page proof in theory that person has spent an inordinate amount of time on the proof and can answer questions, describe some insight, etc etc.
If a random person is given a 60 page proof to digest and not the author, those hidden insights that _aren't_ in the paper might be completely inaccessible. Maybe the AI will "just" be able to provide the insights. Maybe. But pedagogy is tricky work, and despite these AIs being able to do all this fancy math we can't get them to write good cover letters yet, so....
Ultimately we might be left with just a bunch of intellectually unsatisfying proofs. This means way less drive to simplify the proofs or rework them.
End result: we generate a layer of "less efficient" mathematics, that won't get built upon. We will not actually have any shoulders upon which to stand.
AI can simplify and rework proofs too.
According to Scott Aaronsson, OpenAI set their agents on 8000 different problems, and got 372 final proofs. Even spending twice the original effort on simplifying and reworking those proofs so that they do not "feel like something written by someone who’s on psychedelics" would only increase the compute by less than 10% (assuming all the agents had a similar token budget).
The fact that they did not do so can only mean that either (1) their agents currently lack the capability to do it, or (2) OpenAI are completely indifferent and do not care in the slightest if the proofs are understood or not.
7 replies →
But why should process of discovering mathematical insights be any less attainable to AI models?
The concern is being raised without evidence, because the evidence points to the gap simply being frontier models have just started to be able to get a raw proof out. Why, given existing progress, should we expect them to be unable to distill insights from those proofs?
Certainly this even more likely doesn't matter at all for applications: if I can send a radio signal further because my AIs design it a certain way, that's an unambiguous result. Which is really the next step here: turn a proof into a "mechanical" application.
> I'm not sure there's any evidence to suggest exploring and refining results is outside their capabilities
OP didn’t suggest that.
The bar has been raised. Everyone has to meet it now. An inelegant solution squatted onto the internet doesn’t count as discovery per se, even if it’s impressive.
A correct solution verified in Lean will count in perpetuum. It is fine if you want more, but an achievement is an achievement, even if it is by AI.
Hmmmm. It feels right that discovery is much more meaningful than achievement. "Bullshit lean proof" or "bullshit achievement" smells like it. "bullshit discovery" smells like a front-handed insult
But what should they do? They got all these proofs, should they just have sat on them?
> should they just have sat on them?
It’s fine that OpenAI posted their findings. It’s not fair to claim these problems have been solved. Not until someone can understand and verify the proof and then communicate the core, novel methodological element to someone else.
But this is Tao's point: Before, the mechanism by which a proof was verified and communicated and digested by the community was for the person who came up with the grotty, ugly first draft to engage with the community. Now there's nobody to really engage with, so the pipeline from "grotty, ugly draft" to "integrated into humanity's mathematical knowledge" has been broken.
So yeah, probably we should stop saying "X has been solved", and instead say, "A Lean proof for X (or !X) has been generated". That doesn't change the fact that incentives are currently on finding the proof, and once the proof is generated by an AI, there's not currently a good mechanism / incentive structure to move that into the mathematical community. AI is here, so we need to find a new mechanism.
1 reply →
Solving a problem is not solving anymore. Up is down, pleasure is pain, darkness is light, slavery is freedom, madness is sanity.
Many of these are lean formalized. Arguably a much higher bar than whatever peer review provides in terms of verification.
2 replies →
>They got all these proofs...
Your phrasing is illuminating that perhaps they aren't engaged in the creation, understanding, or integration of these proofs by humanity; they just have them. For them, this is a slidedeck they can pass to investors, creditors, the marketing department. Something they can add to the employee onboarding pamphlet.
What should they do? Hyperbolic maybe, but perhaps engage with humanity.
...they did.
No need. In the end the mathematicians that don't like this can just not look at the proofs or use them. They have that choice. Just like they didn't "ask" for them, they don't have to even acknowledge they exist.
BlackBox: The proof is in the pudding
This isn't only bad for Math — it's bad for English too.
'Proof' is going to become the 2026 Most Misapplied Word of the Year.
At least check them properly. They have already withdrawn some of them.