271–280 of 607 posts
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This isn't brute force.
It is in the same way that educated guessing is.
Here is the chat: don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem. {{problem}} REMEMBER - this unconditional argument may require non-trivial, creative and novel elements. Then "Thought for 80m 17s" https://chatgpt.com/share/69dd1c83-b164…
>don't search the internet. I think this was key. Otherwise the LLM could think it can't be done.
Here is the chat: don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem. {{problem}} REMEMBER - this unconditional argument may require non-trivial, creative and novel elements. Then "Thought for 80m 17s" https://chatgpt.com/share/69dd1c83-b164…
Asking the llm to structure its response in plan and implementation, allowing it to call tools like python, sage, lean etc.
I will get downvoted for this but I can't help thinking that billions of dollars have gone into chatgpt over a period of years and an LLM can direct all its "attention" (in a metaphorical sense) on one problem. I think if you gave top mathematicians a few million (so a fraction of a percent of chatgpt budget) to solve this problem over four years, they probably would have at least made significant progress. I don't t…
It seems like alot of scientific advancements occurred by someone applying technique X from one field to problem Y in another. I feel like LLMs are much better at making these types of connections than humans because they 1) know about many more theories/approaches than a single human can 2) don't need to worry about looking silly in front of their peers.
> It seems like alot of scientific advancements occurred by someone applying technique X from one field to problem Y in another. Yeah, you should look into the Langlands project sometime
For the uninitiated, Paul Erdős was a pretty famous but very eccentric mathematician who lived for most of the 1900s. He had a habit of seeking out and documenting mathematical problems people were working on. The problems range in difficulty from "easy homework for a current undergrad in math" to "you're getting a Fields Medal if you can figure this out". There's nothing that really connects the problems other than…
> Each time there's a new model release a few more get solved. I'm no expert, but based on the commentary from mathematicians, this Erdős proof is a unique milestone because the problem received previous attention from multiple professional mathematicians, and the proof was surprising, elegant, and revealed some new connections. The previous ChatGPT Erdős proofs have been qualitatively less impressive, more akin to l…
Interestingly, it was an elegant technique, but the proof still required a lot of work.
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Wait, what do you mean "LLMs are still absolutely useless at actual maths computation"? I rely on them constantly for maths (linear algebra, multivariable calc, stat) --- literally thousands of problems run through GPT5 over the last 12 months, and to my recollection zero failures. But maybe you're thinking of something more specific?
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Capitalism already is a poor allocator of human effort, resources, and energy, why lock in on this specifically? There's entire professions that are essentially worthless to society that exist only to perpetuate the inherent contradictions of this system, why not focus more on all that wasted human effort? Or the fact that everyone has to do some arbitrary sellable labor in order to justify their existence, rather th…
> Capitalism already is a poor allocator of human effort, resources, and energy, why lock in on this specifically? It's absolutely best allocator of human effort there is. It has some problems but compared to alternatives it's almost perfect.
> “The raw output of ChatGPT’s proof was actually quite poor. So it required an expert to kind of sift through and actually understand what it was trying to say,” Lichtman says. This is how I feel when I read any mathematics paper.
The formulas were opaque, notations unique and unconventional, terms appearing out of nowhere, sometimes standard techniques (like 'we did least-squares optimization') are expanded in detail, while other actually complex parts are glossed over.