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Comment by rtpg | Hacker News Reader

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.

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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.

> 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.

Come now, this is kind of unreasonable. When you're working on a new technology, you first get the ugly, inconvenient-to-use prototypes functioning with the core new thing you need; then you work on packaging it up into a format useable in production. I'm sure the very first digital camera sensors weren't very useful for photographers either; but it isn't really even possible to build the rest of the technology required to turn raw output of a digital sensor into something a professional photographer can use until you have the raw output itself.

The research is still on going on the raw output; getting things to the next stage, where the results are widely useable by professional mathematicians (and then on to engineers and scientists to whom the results would be practically useful), is a whole new research area.

Seems like you are just subscribing to the first option I gave, "their agents currently lack the capability to do it", but saying you think they will be more capable in the future if they can move away from the inconvenient-to-use prototypes after more research. Thinking it might be possible in the future is not in disagreement with anything I said, so I am not sure what you thought was unreasonable about my description.

Imagine someone looking at digital camera researchers showcasing a ground-breaking new sensor, and reacting by saying "Well obviously they're completely indifferent and do not care in the slightest if their work is used by real photographers or not."

Like, "Orr... maybe they care a lot, but haven't gotten to that part yet?"

You are conflating the two options with each other (lack of capability vs indifference). One of them is true, not necessarily both ("or", not "and"). I did not claim a lack of capability was the same as indifference.

Or (3) they feel a need to publish first, and that goal takes precedence over (2).

They claim each result used three hours of compute on average. Even spending significantly more on simplifying and reworking would delay the release with a single day at most. If avoiding such a minor delay took precedence over (2), I think "indifference" is the correct term. It has also been a while since the release now, so there is ample opportunity to post follow ups if time pressure was the only concern.

Why do that when they can spend more hours extending QRH to a proof of the full Riemann Hypothesis? The opportunity cost of digging up small potatoes is the whole enchilada.

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.

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