Comment by izzydata
4 days ago
I still think mathematicians are going to be as important as ever. The LLMs are only finding what was technically possible given our current breadth of knowledge after brute force solving problems. Eventually it will run out of things that it can do with its training and the only way to get it to do more will be training it on new human found knowledge.
Finding that new knowledge may be exponentially more difficult, but it will be much more valuable.
> Eventually it will run out of things that it can do with its training and the only way to get it to do more will be training it on new human found knowledge.
How do you know this?
AIs cannot invent things like cubism, surrealism or hip-hop.
Or maybe it can; the early image generators famously did output horrific images sometimes because of their limitations, but these outputs qualify nonetheless creations.
Now the interesting thing is that it is humans who evaluate them as horrific, worthless or interesting.
Certainly AIs could pretend they have that sort of opinions and judgement, but hopefully humans will remain more interested in the opinions of other humans.
> Certainly AIs could pretend they have that sort of opinions and judgement, but hopefully humans will remain more interested in the opinions of other humans.
Online, how would they even know? Offline -- either we give up on the internet, or the offline discussion will be heavily influenced by what AI said online.
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I don't see how its output possibilities could be infinite given a finite set of data. Taken to the extreme if you give an LLM only a single piece of information then that is going to be the only thing it can produce. Given it two pieces of information and maybe it can produce every combination of those two things. Given all of the worlds knowledge I'm sure its possible outputs are incomprehensibly large, but still not infinite. Then having its outputs match a set of really specific instructions is going to be a small subset of that.
How is this different from human brains being made up of a finite number of neurons in a finite number of configurations? I know very little about LLMs and nothing about neurology and maybe you can explain to me why one is so much more powerful than the other.
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Sure, a given LLM can only produce so much (though it might be a lot), and then you'll need fresh inputs. But you contend that those have to be human, while I am arguing that they could be
- random,
- from the environment,
- from other AIs.
That increases the space considerably.
In particular, note that your argument also applies to humans: A human, being finite, can only produce finitely many things. But you add other humans, the environment, and pure chance to the mix, and it'll be pretty infinite for all practical purposes.
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There are two reasons:
1. LLMs aren't run deterministically - they use a bit of noise to improve the output. So even with the exact same input you're going to get a whole distribution of outputs.
2. Feedback from the environment. LLMs (and humans!) work best when they can test ideas. That's why coding agents work so well. If you ask an agent 1000 times to just think of a compression algorithm, it'll probably spit out very samey answers just like a human would. If you give it a test corpus and let it try out different things it will absolutely be able to come up with novel ideas.
Well humans do that and you expect them to continue to do that - why can't AI models do it as well?
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I don't think AI will continue growing infinitely either, but maybe "incomprehensibly large" is large enough to solve all the math problems.
The set of data will increase as it outputs
I liked reading an essay by mathematician Nestor Guillen that develops thoughts along these lines - the "convex hull of ideas".
https://birdsnfrogs.github.io/2026/09/12/Felix_qui_potuit_re...
Yeah, I think that's a great essay and it really helped clarify some of my own ideas.
At the same time, I think it's pretty amazing how this is the fundamental question of AI's trajectory, yet people on both sides seem so sure of their viewpoint with little actual evidence or data to back it up.
That is, it's possible that LLM-based approaches will be forever limited to this "convex hull" of current training data, and thus humans will always have a role to play (and will retain primacy when it comes to overall intelligence), because it appears that humans are not limited to this convex hull based on previous discoveries (e.g. I think basically every scientist would argue Einstein's general relativity was outside the convex hull that existed at that time).
Yet, if LLM-based approaches are eventually able to surpass humans on this "novel discovery" axis, then we as a species are basically done for when it comes to intellectual primacy - and then it becomes a very strange and scary world. And many AI researchers at the top companies clearly believe current approaches will scale and eventually (pretty soon I'll add) lead us to RSI.
I have no idea which side is right, and I'll admit I really hope LLMs eventually hit a wall. But again, I just am surprised that many seem to be putting forth their beliefs, but I would love to know if there is any good evidence one way or the other (or better yet, a more concrete and verifiable definition of the "convex hull" so that researchers could provide some falsifiable examples).
Came here to say this. What AI is doing with math is essentially fuzzing, but looking for valid inputs that solve a problem and the inputs are mathematical abstractions. It's a cool approach, but AI doesn't understand what's going on, and without understanding it won't be able to create the next generation of mathematical abstractions needed for the next generation of proofs.
this is assuming that humans can be original in ways llms won't be, which I doubt will hold true
> which I doubt will hold true
Why?
Because I don’t think there is any fundamental computation we can perform that ai can’t
[flagged]
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aren't mathematicians needed to create the problems? Everything solved so far is a question posed by a human. Which is probably why cracking diseases is more difficult (apart from man made viruses :/)