>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.
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?
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.
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.
>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
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.
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?
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?
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?
HEH. Don't know why you're getting downvoted. It's painfully obvious that there is a vicious AI backlash now, where every amazing advancement is met with denial and loathing.
Oh wait, sorry, I do know why you're getting downvoted. Fear.
A lot of people who thought they were special and “better” than mere blue-collar workers are realizing that in fact;l they are the same just working with a different medium.
Humans just want to be able to work and feed their families. Notice how this is something that is never addressed for example in Asimov's writings where robots do everything. How do people do anything to be able to afford these robots? How do Solarians make money to maintain their massively gigantic estates? It is never explained, but we always jump straight to the "robots do everything, everything is free, nobody works". How about the in between?
Oh yes, I agree entirely. I look at The Jetsons or Star Trek, and I see the fruits of technology shared by all of humankind.
But if the current trends continue, Elon will own all of the robots and the rest of us will be at his mercy.
How we change that - I don't know. But I do know we don't change it by putting our heads in the sand. AI is here and it is real. We MUST take it seriously. Shunning is not a viable option.
We're going to have to (collectively at some point) decide that we shouldn't tie survival to working.
Whether that's UBI, or Fully Automated Luxury Gay Space Communism, or UBS, or some AI managed economy, or some other such thing, we need to decide that "hey, we don't want to tied survival to output under our current system."
That's really the Rubicon we have to cross, and there are a LOT of people who can't really come up with a better way in their own heads yet.
Look, we all saw how things can be during the pandemic. That was a dark time, but it also gives us a model, we can just... do things. We just have to decide to do them.
Oh! Damn! Stupid me! "We have to collectively decide this", when is the meeting to vote on that again? When is the last time we all decided something collectively?
WTF does the pandemic have to do with this? "dark time", oh yeah, people stuck at home watching Netflix, what an incommensurable suffering!
Buddy, I can admire the naive childish optimism to a degree, but come on. "We just have to all decide". Do you live in a Disney movie?
>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.