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Comment by asimpletune | Hacker News Reader

> All this new knowledge is arriving at a pace much greater than the field’s ability to process it

That’s the whole issue: it’s not knowledge, it’s data. AI can not provide an account for the proofs, or be questioned about them, or organize a talk exposing the idea because there’s no understanding behind any of it.

This is what Tao has been saying; that the results, in the strictest sense, were never the goal. It is ultimately the understanding (that previously was required to form a proof) that is valuable.

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Why wouldn’t the AI be able to answer questions about the proofs or organize a talk? Those are pretty much the things it excels at, exploring and summarizing previous knowledge. The problem is the volume of questions and data a human needs to step through to arrive at the same understanding.

Apparently, the knowledge isn't in the data set, and the explanations are gobbledygook. They certainly summarize well, but it seems that if the "understanding" isn't already baked in, then expanding the source description doesn't really clarify it. Maybe in the future?

What does apparently here mean? Is there an account of an expert sharing their attempts to get a model to explain the results and key ideas to them (for a topic they're familiar with) in an interactive session, and having it fail?

For somebody deeply familiar with a topic and all the nuance around the problem and approaches that didn't work, I'd be quite surprised if they couldn't cajole it into explaining what finally did work in terms they understand. Unless it turned out that these proofs were just well beyond anything humans were anywhere near being able to figure out, in which case, no great loss that the AI figured it out because we were nowhere near it.

> explanations are gobbledygook

To humans? To check if the explanations actually make sense we would have to pause the new AI in while it's rediscovering the result and steer it with the explanation to see if it arrives at the result faster or slower/same.

It very well may be that explnations need to be further explained until they don't sound like gobbledygook to humans. If that's harder than arriving at the result then it's a sign of how far ahead AI actually is.

Yes. These explanations are possible and will improve. For example: https://youtu.be/mtU4op2kMWI?is=Tr-d91BvFEsVNmiL

Fair, “answers” is probably more precise than “knowledge.” That gap between answers and understanding is the whole point of the post, so I think we mostly agree.

> It is ultimately the understanding

But understanding to what end? I'm if it's for the pure aesthetic experience of engaging in the beauty of math than that's fine, but that's typically not the view from my experience.

The goal of understanding is to advance the field, since historically human understanding was the only way to do this.

For the vast majority of human history, the world we experienced was a strange and unintelligible space. Humans survived at the by the grace of forces beyond their control. For a brief window of time human existed in a world where they increasingly saw a relationship between their understanding of the world and there ability to steer their environment towards a desired outcome.

I believe now we're seeing that that was a historical anomaly. The world is once again entering a state where it becomes increasingly unintelligible to us. Nick Land already famously pointed out, many decades ago, that the global financial system is already a form of "artificial intelligence" we don't really control. We're seeing that spread wider and wider.

The world making sense peaked around 1960s and has continued to breakdown ever since.

Does that mean AI is not doing something useful? If it provides a proof, it gives direction to human mathematicians who can then develop an understanding, give talks, be questioned about the topic, and teach. Is that not a useful service?

I don't think that's the argument. In my opinion this is like paying to unlock characters, à la EA. Who's going to feel a sense of accomplishment by just trying to interpret what an LLM spat out? Sure,maybe the results will be used by someone in some field, the same way a product manager uses what the development team developed. Is the PM going to give talks about it? Are they going to expand on those developments and come up with something new?

> Who's going to feel a sense of accomplishment by just trying to interpret what an LLM spat out?

I think you have a point, but this is the reality we have to face. The genie is out of the bottle. Even if OpenAI stops publishing AI-generated proofs, it's only a matter of months before tools with similar capabilities are in everyone's hands.

You're right.

Hopefully, this genie will grant us a few wishes

It might well be useful if the RIGHT proofs are evaluated and proven. Figuring out what will be useful has always been a real challenge in math. Finding certain symmetries and mappings between problems in different domains, might well be useful even if they aren't well understood? That has always been another part of the work of mathematicians. Of course there are those who just work on the beauty of things, and few in the 80s would have thought that prime factoring number theory or elliptic curves would be the basis for modern communications and banking.

That said, getting a point solution and not knowing the path to get there, is certainly much less useful, and generalization is much harder. Again, more work for mathematicians, but maybe without the easy "I solved it" proof metric for rewards. Goodhart's law strikes again.

Less useful, but still useful. If robot Ramanujan gives us answers with no mortal-understandable justification, but it's always right, that still gives decades or centuries of topics to try to build theory around, with the motivational benefit that you always know that what you're working on can be solved. Simply treat it as an oracle that dispenses magical opaque proof certificates.

it's data for humans its knowledge for AI. they might be able to process it understand it and build upon it even further

I guess the issue with that is that the understanding is important to mathematicians. The majority of people outside mathematics don’t understand it whether it’s humans doing the work or AI. If AI can generate useful results more quickly, then to the general public it is more valuable.

Mathematical solutions aren’t valuable to the general public at all, other than the passing fancy that comes from reading headlines and news articles.

Mathematics is only useful to the extent that we can do something with it, and I would guess that still requires human mathematicians to understand it.

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