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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
#102Re: An OpenAI model has disproved a central conjecture in discrete geometry
#103Earlier quoted context omitted.
I'm not a scientist but I like to LARP as one in my free time, and I have found ChatGPT/Claude extremely useful for research, and I'd go as far as to say it supercharged it for me. When I'm learning about a new subject, I'll ask Claude to give me five papers that are relevant to what I'm learning about. Often three of the papers are either irrelevant or kind of shit, but that leaves 2/5 of them that are actually usef…
One heuristic I used during my masters degree research thesis was to look for the seminal people or papers in a field by using google scholar to find the most cited research papers and then reading everything else by that author / looking at the paper's references for others. You often only need to go back 3-4 papers to find some really seminal/foundational stuff.
Yeah, that's actually how I discovered Leslie Lamport like ten years ago. I was looking for papers on distributed consensus, and it's hard not to come across Paxos when doing that. It turns out that he has oodles of really great papers across a lot of different cool things in computer science and I feel like I understand a lot more about this space because of it.
It doesn't hurt that Lamport is exceptionally good at explaining things in plain language compared to a lot of other computer scientists.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#104Re: An OpenAI model has disproved a central conjecture in discrete geometry
#105Earlier quoted context omitted.
> I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. Most discoveries are indeed implied from axioms, but every now and then, new mathematics is (for lack of a better word) "created"—and you have people like Descartes, Newton, Leibniz, Gauss, Euler, Ramanujan, Galois, etc. that treat math more like an art than a science. For example, many belive that to…
what basis do you have for assuming an LLM is fundamentally incapable of doing this?
Because by definition LLMs are permutation machines, not creativity machines. (My premise, which you may disagree with, is that creativity/imagination/artistry is not merely permutation.)
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#106As I have stated before, AI will win a fields medal before it can manage a McDonald's A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation. LLMs are just the beginning, we'll see more specialized math AI resembling StockFish soon.
the only thing keeping the mcdonalds from happening will be political, likewise the same with fields medal
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#107To the “LLMs just interpolate their training data” crowd: Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules. I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. So either “recombining existing material” isn…
I think you are conflating composition and prediction. LLMs don't compose higher abstractions from the "axioms, symbols and rules", they simply predict the next token, like a really large spinning wheel.
How sure are you that this is correct?
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#108I dunno, I'm skeptical without proof. I've had the MAX+ plan for a while and I'm sorry, the quality between GPT vs Claude is night and day difference. Claude understands. GPT stumbles over every request I give it.
Weird thing to say about a report which literally has the attached mathematical proof.
Except its not a proof. It's an existential proof of what? Projecting points and loosing density? Nah, it's wrong. At least with Edros you could solve f(x) or not solve it (inf). You can not with this. All they did was balance a really fancy quadratic equation. The projection from C^f to R² doesn't demonstrate geometric injectivity, so nⱼ = |X| isn't established, and the bound collapses.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#109To paraphrase Gwynne Shotwell: “Not too bad for just a large Markov chain, eh?”
Erdos, or the model?
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#110AI isn't going to supercharge science but I wouldn't be as dismissive as other posters here.
Not only it supercharged science it supercharges scientist. Research on any narrow topic is a different world now. Agents can read 50 papers for you and tell you what's where. This was impossible with pure text search. Looking up non-trivial stuff and having complex things explained to you is also amazing. I mean they don't even have to be complex, but can be for adjacent field where these are basics from the other f…
It's a very heavy hammer. I used it in the way you describe and after double-checking noticed some crucial details were missed and certain facts were subtly misrepresented.
But I agree with you, especially in areas where they have a lot of training data, they can be very useful and save tons of time.