[qsera]

From the post lol

>So I wouldn't really say that this result is using or creating some fundamentally new techniques in convex geometry or optimization theory. What this means from my perspective is that if a result is attainable with existing techniques, modern AI methods will be able to solve those problems. I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed.

[WA]

If knowledge is a Swiss cheese, LLMs can help fill the holes, but not make the cheese bigger.

[peddling-brink]

Today maybe. I disagree in the long term.

While they’ll never have the same subjective experience as humans, what stops an LLM from applying similar lines of thought* in a manner that results in a novel conjecture?

They are prediction machines, and so are we in a way. We can give them nearly limitless resources to scale their predictive capabilities. We have billions of years of training baked in. They distill directly from our knowledge and can walk down paths that no human has before.

It’s silly to say they’ll never do anything novel.

At their current capabilities, it sounds like they are already capable of being a specific type is research assistant. What will that look like in 10-20 years?

[seiferteric]

They also have ability to go deep and wide in a way that humans just can't. We have limits, get tired, distracted and biased where AI does not. I think there a lot of problem where all the information needed to solve them is there, but we just can't put the pieces together. Like no matter how many people you throw at some problems, you hit human limits and more people won't help, but AI will because it is just relentless.

[qsera]

>biased where AI does not.

AI can be totally biased...

The fact that it can spout bullshit all day long to a human who can be tired and would actually act on the said bullshit, is not very comforting...

For example, an LLM could confidently declare something a tired human would take as a fact, but would backfire in a real world.

[seiferteric]

Not really the kind of biased I meant though. There was a recent article about a AI disproving I think an Erdos conjecture by doing similar things humans have tried, but it was much messier and less "beautiful". I think it is a common bias in science and math that things should be "beautiful" but there is no real reason to think that.

[qsera]

>what stops an LLM from applying similar lines of thought* in a manner that results in a novel conjecture?

One thing is that an LLM can never assume, or find out, an inconsistency in its training data. Novel ideas often require correction of existing assumptions. As far as I understand, it is impossible, by design, for LLMs to contradict what is in its training data.

For example, an LLM trained on the data from an internet comprised of people who believe in the earth centric hypothesis can never say "Hey, that cannot be correct", or come up with the heliocentric alternative

But maybe it is not applicable to pure Math...

[WarmWash]

They can, but it's limited to that specific chat context.

[qsera]

They can spot contradictions in the the prompt. But not in their own training data.

[qarl2]

> While they’ll never have the same subjective experience as humans

You state this as a fact - are you aware the question is unresolved?

EDIT: I'd love to know why you're downvoting me for stating a known fact.

[peddling-brink]

Ok, I guess never is a real long time and eventually when we merge our consciousness with the machines we may have the same subjective experience.

I can confidently state that GPT-5.6 Sol is not experiencing the same reality as me. They _might_ be "experiencing" and I personally think they are, but their reality and experience is not the same as ours.

[qarl2]

Well, sure. I'm not experiencing the same reality as you, either. I guess I assumed you were implying something more - a lesser experience or something. No?

[skeledrew]

Fear spreads.

[ben_w]

Famously, all of maths is axioms and tautologies, so I'm not sure this will assuage any professional mathematicians currently having an existential crisis.

Maths was already infinite, it's still infinite, but who wants to spend all their lives changing rooms inside Hilbert's Hotel?

[throw310822]

The author explains he's an expert in the domain and that he had worked sporadically on the problem for about a year, also with the help of previous LLMs. So whatever he means by "I wouldn't really say that this result is using or creating some fundamentally new techniques" it doesn't mean that the result was trivial. Also, says it might not make sense to work on low or even medium hanging fruits in the future- and I bet that's by far the largest share of work for most mathematicians.

Sure, it's not a breakthrough that opens new roads in mathematics- is this where the goalpost has moved now?

[tripleee]

this is a fairly bleak outlook even when you're trying to make it sound the opposite. Only the cream of the crop talent will have value going on?

Most of us aren't Terence Tao

[monster_truck]

so it seems like The New Big Question In Math is

How's It Hanging, Brother?