AI is the interpolation of the human corpus. Is it suprising AI recombines sucessfully where human attention has not explored all plausible solutions? N,o not especially. The key fallacy is that AI is other than human. This is really no different from computer proofs, e.g. 4 color theorem. The fact the prompt is not linked to the solution by individual human intention alone does not make the solution less human in origin.
Mathematicians issue warning as AI rapidly gains ground
171–180 of 366 posts
Re: Mathematicians issue warning as AI rapidly gains ground
#172I'm curious about whether we will start discovering new maths in the next few years that provide insight into unsolved CS or Physics problems!
For all you know, some of this has already happened but kept secret for national security reasons
Well, we had tried to ban exporting cryptography once. It didn't go well.
Re: Mathematicians issue warning as AI rapidly gains ground
#173I'm curious about whether we will start discovering new maths in the next few years that provide insight into unsolved CS or Physics problems!
I think it's going to reduce the friction of exploring new areas in math, and that we're going to see a golden age of math unlike anything seen before.
Right, most professional mathematicians know almost nothing about their neighboring branches of mathematics.
An algebraic geometry researcher would be hard pressed to understand a new result from category theory or even something closer like commutative algebra.
Re: Mathematicians issue warning as AI rapidly gains ground
#174One of the reasons why over a decade ago, I dived deeply into the OSS world instead of mathematics was that it was so much more accessible: there were docs for everything, and I got direct feedback when something worked vs when something didn't work. Most of my questions had answers on stack overflow, and once I joined Rust (which back then in 2015 didn't have a big stackoverflow presence) I had a community who answered them for me (and in maths I didn't have that).
AI makes the math world more accessible than before. If you have a question about a proof in the lecture, you can just ask it. Of course, one can't trust it blindly, but fundamentally it's amazing.
I think that's a good thing, but of course this means that a lot has to change in culture and behaviors, also in the research world.
The software engineering world is more or less in the same situation, it's also changing. But for now I think it still holds true that someone who knows maths plus an LLM is better than someone who doesn't know maths plus LLM. At least in software it does.
Re: Mathematicians issue warning as AI rapidly gains ground
#175[flagged]
Re: Mathematicians issue warning as AI rapidly gains ground
#176Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public. Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question. The annoying thing about recent AI advances is that they target questio…
To me, the most interesting feature of the OpenAI solution of the Unit Distance (Erdös) Problem is that the solution - using deep algebraic number theory as a source of extremal combinatorial/geometric constructions - is much more interesting than the problem’s elementary statement might lead one to expect. Writing off Erdös’s problems as random, useless, or meaningless dismisses his mathematical intuition, second-to…
I don't think Erdos problems are useless myself, I put "useless" in quotes to emphasize that they are the sort of research that doesn't have an immediate application, and so their automated resolution should be weighed against the sociological cost.
As opposed to, say, drug discovery.
Re: Mathematicians issue warning as AI rapidly gains ground
#177One of the reasons why over a decade ago, I dived deeply into the OSS world instead of mathematics was that it was so much more accessible: there were docs for everything, and I got direct feedback when something worked vs when something didn't work. Most of my questions had answers on stack overflow, and once I joined Rust (which back then in 2015 didn't have a big stackoverflow presence) I had a community who answe…
I imagine the concern is more towards using LLM's to create proofs rather than using them to understand things.
Re: Mathematicians issue warning as AI rapidly gains ground
#178Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field. Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI gene…
Much like for many the point of chess is that it's played by humans, with truly superhuman AI relegated to a training aid, mathematics is in many ways about human comprehension. You can use AI to find and proof new theorems. But if you get to the point where humans can't understand it, is it even still math?
Neural networks are already systems of linear algebra that are beyond human understanding. Most humans could probably grok a 1 or 2 dimensional slice of a network, but the latent vector space is completely beyond the human brain. We have to use tools to analyze neural networks piecemeal in exactly the same way that we analyze any other higher-dimensional construct. Few humans are truly capable of reasoning in 4+ dimensions, that doesn't make string theory "not math". Nor does a trillion-dimension vector space of an LLM make it "not programming".
Humans by themselves invented mathematical concepts beyond human understanding a long time before we invented neural networks.
Re: Mathematicians issue warning as AI rapidly gains ground
#179Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field. Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI gene…
On the other hand, it could stall out at: good enough to take the easy problems, not good enough to take over the field, but damaging enough to erode the quality of new entrants. (Which incidentally is the scenario I think plays out for software)
Re: Mathematicians issue warning as AI rapidly gains ground
#180Anyone else draw similarities with this and the artists and authors who complained when gen ai first came out. I think a lot of people don't realise the disruption ai will cause to many industries, until its directly impacting them, basically personal fable at scale ( https://en.wikipedia.org/wiki/Personal_fable ).
The artists will be fine and AI will liberate them. It's the engineers and mathematicians who are walking into the blade. They built their entire sense of self on being the best optimizers in the room and optimization is the first thing the machines take. Their whole identity was a number going up. Now watch it go to zero.