I see mixed emotions here. I understand both. On one hand it's exciting and fascinating. On the other it's concerning. One concern I haven't seen mentioned is the possibility that, as these models become larger and more powerful, their capability to solve frontier math problems will also grow. Does there become a point where humans are no longer the driver of innovation and research in this world, and instead are relegated to become stewards of the AI models whose purpose is to push the boundaries of mathematics, theoretical physics and other academic disciplines?
An OpenAI model has disproved a central conjecture in discrete geometry
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Re: An OpenAI model has disproved a central conjecture in discrete geometry
#542I think one interesting thing to point out is that the proof (disproof) was done by finding a counterexample of Erdős' original conjecture. I agree with one of the mathematician's responses in the linked PDF that this is somewhat less interesting than proving the actual conjecture was true. In my eyes proving the conjecture true requires a bit more theory crafting. You have to explain why the conjecture is correct by…
That's proof by contradiction: https://en.wikipedia.org/wiki/Reductio_ad_absurdum
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#543I see mixed emotions here. I understand both. On one hand it's exciting and fascinating. On the other it's concerning. One concern I haven't seen mentioned is the possibility that, as these models become larger and more powerful, their capability to solve frontier math problems will also grow. Does there become a point where humans are no longer the driver of innovation and research in this world, and instead are rel…
For those of us who care about the answers to these questions, rather than who gets credit for doing it, we will welcome any faster means of solving these problems.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#544[flagged]
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#545I see mixed emotions here. I understand both. On one hand it's exciting and fascinating. On the other it's concerning. One concern I haven't seen mentioned is the possibility that, as these models become larger and more powerful, their capability to solve frontier math problems will also grow. Does there become a point where humans are no longer the driver of innovation and research in this world, and instead are rel…
I believe that the answer is yes it will happen... the question is when will that point will occur.
Right now, we are in a transition period... Models are improving, but they are not capable just yet to take over.
Where do you see it being in a years time? or 2? or 5?
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#546Seems rather depressing to me but maybe I am a Luddite.
Exactly. I would rather we let these discoveries stay hidden for a while longer such that human ingenuity may untangle them from the coils of reality. A machine? A mechanical man? Deins to produce something as pure as mathematics without the divine fervor of the ineffable spirit of Man?! It's just not what God wants.
I can't tell if this is satire.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#547Re: An OpenAI model has disproved a central conjecture in discrete geometry
#548Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…
I cannot quite share your enthusiasm. The clearest analogy that I can think of to try to explain why I feel this way is that it seems there will eventually be a phantom textbook of all of mathematics contained in the weights of an LLM; every definition, every proof, etc; and the role of a mathematician is going to be reduced towards reading certain parts of this phantom textbook (read: prompting an LLM to generate a…
It’s funny because the shift from handmade goods to automated factories didn’t seem so bad. Same for mechanized farming instead of mules and people.
Shifting from “human calculators” to machines for arithmetic is also hard to argue against.
I think what makes the AI transition difficult is it impacts a wide range of high-value activities that would have been implicitly assumed to always remain human.
I do have great trouble seeing how a pile of matrices is ever going to be capable of innovation. Maybe with sufficient entropy and scale, it will… The day that becomes practical will be a turning point in history.
Economically, goods and services are often priced based on labor/“value added” aspects. Lawyers’ fees aren’t driven by paper costs! If AI takes a huge bite out of intellectual labor, the future could become very different…
BTW, your book description reminds me of the 2025 movie “A.I”. I thought it was quite good.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#549Earlier quoted context omitted.
Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.
Because for many people who pursue these fundamental truths, the reward is not necessarily personal fame, fortune, or even personal understanding. Advancing humanity's total knowledge (even if that knowledge is by proxy through AI) is reward enough.
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Re: An OpenAI model has disproved a central conjecture in discrete geometry
#550Earlier quoted context omitted.
Exactly. I would rather we let these discoveries stay hidden for a while longer such that human ingenuity may untangle them from the coils of reality. A machine? A mechanical man? Deins to produce something as pure as mathematics without the divine fervor of the ineffable spirit of Man?! It's just not what God wants.
I can't tell if this is satire.
I had the exact same thought. It depends entirely on what voice you read it in, I suppose.