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Amateur armed with ChatGPT solves an Erdős problem

scientificamerican.com

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Re: Amateur armed with ChatGPT solves an Erdős problem

#371

Post by miyoji »

pglevy wrote: post #370
andrepd wrote: post #347

Earlier quoted context omitted.

The simulacrum of a thing is not the thing! Not only is the "interesting!" unrelated to any "thought process", the whole """thinking""" output is not a representation of a thought process but merely a post-facto confabulation that sounds appropriately human-like.

Can't help but think of this I re-read recently from Nietzche: > When I analyze the process that is expressed in the sentence, "I think," I find a whole series of daring assertions that would be difficult, perhaps impossible, to prove; for example, that it is I who think, that there must necessarily be something that thinks, that thinking is an activity and operation on the part of a being who is thought of as a caus…

That is saying something completely different from the comment that you're responding to, though.

Re: Amateur armed with ChatGPT solves an Erdős problem

#373

Post by balamatom »

bonesss wrote: post #249
burnerRhodov2 wrote: post #225

Earlier quoted context omitted.

Just the right "prompt" is exactly what happened here. Lean has been developed and incorporated into it's data set. Also, token responses only vaguely correlate to "human language" and it's been proven transformers develop their own internal representation that has created a whole field called machanistic interpretation. Being able to more correctly "parse", AKA using Lean and the right "Prompts, insights and suggest…

> machanistic interpretation Awesome term/info, and (completely orthogonal to whether they’ll take err jerbs ): I’m really excited about the social/civic picture that might be enabled by a defined and verifiable ontological and taxonomical foundation shared across humanity, particularly coupled with potential ‘legislation as code’ or ‘legal system as code’ solutions. I’m thinking on a time horizon a bit past my own l…

Moldbug called, asked for his mold and bugs back.

Re: Amateur armed with ChatGPT solves an Erdős problem

#374

Post by FrustratedMonky »

lqstuart wrote: post #363

Buried pretty deep in the article > “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. But now he and Tao have shortened the proof so that it better distills the LLM’s key insight. I guess “ChatGPT came up with a novel approach to a problem that later turned out not to be totally stupid and ter…

How often are humans initial key insights, also sublimely distilled and beautiful.

This is like comparing someone's first draft, with a final published paper.

Re: Amateur armed with ChatGPT solves an Erdős problem

#375

Post by arcticfox »

lqstuart wrote: post #363

Buried pretty deep in the article > “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. But now he and Tao have shortened the proof so that it better distills the LLM’s key insight. I guess “ChatGPT came up with a novel approach to a problem that later turned out not to be totally stupid and ter…

That should be buried, I agree 100% with their headline and structure over yours.

For comparison, if the amateur did it by hand but the result was sloppy to read, would you prefer "Amateur solves an Erdos problem" or "Amateur came up with a novel approach to a problem that later turned out not to be totally stupid and terrible for once"?

Re: Amateur armed with ChatGPT solves an Erdős problem

#376

Post by Calazon »

pontifier wrote: post #297
teiferer wrote: post #198

Earlier quoted context omitted.

Every model is able to solve each problem, given the right prompt. (Worst case, the prompt contains the solution.)

Interesting... Exhaustive brute force prompting might expose previously unknown capabilities in existing models. Seems like a whole can of worms.

Exhaustive brute force prompting is completely unfeasible. The number of potential prompts is impossibly large.

Re: Amateur armed with ChatGPT solves an Erdős problem

#377

Post by instakill »

shybear wrote: post #139

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.

Isn't this just how Von Neumann would innovate?

Re: Amateur armed with ChatGPT solves an Erdős problem

#378

Post by arcticfox »

chvid wrote: post #273
adamgordonbell wrote: post #3

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…

I am curious if there is a “harness” for maths out there (like the system prompt and tool collection in Claude code but for maths instead of coding)? Asking the llm to structure its response in plan and implementation, allowing it to call tools like python, sage, lean etc.

I am not part of the scene but I am sure there is, Tao himself talks a lot about this type of thing

Re: Amateur armed with ChatGPT solves an Erdős problem

#379

Post by JonChesterfield »

You too can solve maths problems by:

1. Generating enormous amounts of text

2. Persuading a mathematician to look closely at it

3. Announcing success if they conclude it is a proof

This is deeply disappointing relative to "chatgpt found a proof that isabelle verifies" or similar, especially the part where a mathematician spends (presumably hours) reading through the llm output.

Re: Amateur armed with ChatGPT solves an Erdős problem

#380

Post by hmontazeri »

bertil wrote: post #336
urutom wrote: post #265

Earlier quoted context omitted.

What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…

> the AI says things like “Interesting!” My experience of those utterance is that it’s purely phatic mimicry: they lack genuine intuitive surprise, it’s just marking a very odd shift in direction. The problem isn’t the lack of path, is that the rhetorical follow-up to those leaps are usually relevant results, so they stream-of-token ends up rapidly over-playing its own conviction. That’s why it’s necessary (and often…

The new Opus 4.7 thinks quite often with: Hmmmm…

Haha anyone else seen this?

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