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PaperclipPerfector  10d ago (text post)   25159 thread views

Culture War Roundup for the week of October 12, 2026

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A model can trivially be trained on every math publication published in the last hundred years, while a human can see only the tiniest fraction of them.

The models already are trained on them, and probably have been since 2022.

All of these discussions cause people to reflect on the process of doing math. They’re like, “Oh, this thing can do this impressive stuff. What does that mean for us?” One of the people in that video highlights this quote: “good mathematicians prove theorems, great mathematicians come up with conjectures, and the greatest mathematicians come up with definitions.” That’s more or less exactly your framing here. We need the conjecture generator and then the definition generator. That’s the premium-tier mathematician.

What is it that causes current models to be great theorem provers and poor conjecture and definition makers? It's unclear, and perhaps this comment will look foolish in six months, but it's not as simple as "train on all the math papers bro".

What is it that causes current models to be great theorem provers and poor conjecture and definition makers?

Assuming that this is true (and I think you are probably right), I would guess that it has to do with the way the model is trained. The easier it is to verify that a correct answer is indeed correct, the easier it is to put together a big pool of training data for an AI system.

So for example, suppose you wanted to train an AI system to create funny jokes. If you had a million jokes and funniness scores for each joke which were precise and accurate, you could probably do it pretty well. But it would be extremely difficult and expensive to construct this kind of training data set.

With mathematical theorems, it's much easier to verify that a proof is correct -- to a large extent it can be automated. Which means that it's much less expensive to train an AI system. By contrast, with conjectures, it's much more difficult to evaluate how good a conjecture is.

Anyway, I am not an expert on AI but that's my guess.

What is it that causes current models to be great theorem provers and poor conjecture and definition makers?

What is the evidence that current models are poor "conjecture and definition makers" relative to humans?

An alternative hypothesis is that this is a case of the "what happens when you post a real Monet and say it's AI?" phenomenon, in which human purported experts systematically downplay the strength of AI capabilities for complicated social / psychological reasons.

Right, the reason we know that models are now better than us at proof is because it's objective and testable. When (probably not if) models surpass us at making conjectures and definitions, I expect us to take a lot longer to acknowledge it. That might have already happened, but we wouldn't see a press release proudly crowing about it; mathematicians would just quietly use AI as a source of inspiration more and more.

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