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Comment by civvv | Hacker News Reader

LLM’s seem very good at solving mathematical problems of which there is an enormous amount of exisiting work/attempts in their training data. This is an amazing capability, but does not convince me that these models are «thinking» or «reasoning» in the way a human does. A human mathematician could in theory categorize/discover an entirely new field of mathematics tomorrow, based purely on their «human intelligence», I wonder if we will see similar examples by LLM’s soon. It seems to me currently impossible that LLM’s can replace human mathematicians, because of their (assumption) likely dependence on human input in the sense of enormous amounts of pre-existing attempts/data.

If an entirely new problem, within a new field of mathematics were to appear tomorrow, I highly doubt an LLM would be useful at all on their own. Is this the «ultimate ASI test»?

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This is also what I've been thinking. The result itself is amazing but it's not like this was completely unexpected. There has been a huge amount of progress on the problem in the last 10 years without which it seems unlikely today's full resolution would have been possible. It is not clear what strategy was taken but it sounds like it borrowed heavily from the two spanish mathematicians. Experts will scrutinize the proof and it will be interesting to see if anything truly original or unexpected was done, outside of known techniques, a move 37.

That doesn't really matter. Currently we're in the "this is a dog" (marks a muffin) stage of "AI as a scientist". It's totally reasonable to expect that considering how rapidly AI is advancing, the frontier of knowledge and research won't be universities anymore, but rather AI companies running their models in a loop.

Imagine that 20 years from now nobody really does science by hand because AI is just better at it, everyone just runs models, but these models require so much memory that only datacenters can realistically handle them, and it just so happens that the public gets access to nerfed models, while privately, companies actually break all asymmetrical encryption ciphers.

If an entirely new problem, within a new field of mathematics were to appear tomorrow, I highly doubt a human mathematician would be useful at all on their own.

How have we got to the place we are today then? Someone must have made the first steps onto uncharted territory, otherwise we would be in a homogeneous state frozen in time.

I am not saying that LLM intelligence can not be the same, that they are uncapable of dicovering new fields/problems that they have no training on. I am just pointing out that historically it kind of "must" be true that humans are capalbe of this, but we have yet to see an LLM do something like this, something radically "new" in a sense. All of these breakthroughs appear to me (not a mathematician) to be more a case of "digging" through millions of existing attempts/work, patching it together into a result.

This would already make LLM's one of the greatest tool mankind has ever made, but it has yet to display what I would consider a necessity for human level intelligence, which is this ability to discover entirely "new" things.

Would an LLM, given enough time and only the currently available trainingdata with no further input from humans, be able to solve something that was discovered tomorrow?

For humans my answer would be: maybe, probably, because this has been done historically.

For LLM's I would not be comfortable in claiming that they could. I think they would not be any better at this than traditional computational bruteforce.

What a weird conclusion to come to looking at the world around you

Extreme temperature levels (>2.0) can push a GPT of its manifold, essentially producing predictions barely distinguishable from random noise (it flattens the probability distribution of the next token). In theory this could predict anything including the next field of mathematics (infinite monkey theorem) but realistically that would never happen.

However, how to we know the next field of mathematics isn't a novel combinations of several other sub-fields? That level of mathematics would be indistinguishable from magic to most people and so in their eyes the GPT did something truly inventive.

The kind of humans who invent entire fields of science on their own come by a few times a generation. It’s fine to say AI isn’t anywhere as close to them in intelligence, but instead is comparable to the “average” mathematician who is building on the work done by others and taking it a bit further.

Yeah, thats likely true to some extent. But my point is perhaps a "counter-thought" to the idea that this is ASI level intelligence and that math is now a computer task and not a human one. If it is incapable of moving maths forwards into the "unknown" it simply can not replace humans, and this might be a hard structural block for LLM's.

A lot of what humans do is combining old ideas.

And an LLM could in theory also stumble upon entirely new ideas: there's randomness in how they generate their reasoning and answers after all.

I suspect that we are seeing a lot of advances coming from the combination of existing but somewhat obscure knowledge coming from LLMs at the moment, because LLMs are really good at this. At least compared to humans.

Even before our AI friends became good, they were already known for having read approximately every paper and every textbook published in any language. You only need to increase intelligence a fairly small amount from there to get to something like the 'convex hull' of human knowledge.

Compare https://slatestarcodex.com/2016/11/17/the-alzheimer-photo/

The gist is that basically whenever anyone comes up with a new method you get a big burst of activity of picking up all the now lower hanging fruit, that was previously out of reach.

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