referring to Tao as just a 'mathematician' gave me a good chuckle
what did you expect?
Amateur armed with ChatGPT solves an Erdős problem
491–500 of 607 posts
Re: Amateur armed with ChatGPT solves an Erdős problem
#492Earlier quoted context omitted.
1) I never said random 2) I never said cherry picking RARE meaningful text 3) It is not false in every example you gave just because you say that it is 4) If I didn't know better, I might think you're confused about what statistical means (hint: it's not random)
No, it's false in each example because I'm either a first or secondhand party to it happening (except for the Erdos thing) and I know it's false. You managed to include in your blanket and conclusory rebuttal "solving undergrad math problems instantaneously". That was one of my examples because (1) it pertains to the subthread, (2) I was talking about it upthread, and (3) I have direct firsthand knowledge. As I said…
That's convenient. But I have a challenge for you if you're brave enough to face your delusions. Paste this into your LLM of choice and see what happens:
"A farmer has 17 sheep. 9 ran away. He then bought enough to double what he had. His neighbor, who had 4 dogs and 14 sheep, gave him one-third of her animals. The farmer sold 5 sheep on Monday and again the next day, which was Wednesday. Each sheep weighs about 150 lbs. How many sheep does the farmer have?"
Re: Amateur armed with ChatGPT solves an Erdős problem
#493Here 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 kind of expected some discourse first. Someone try the prompt with P=NP in the {{problem}}
Re: Amateur armed with ChatGPT solves an Erdős problem
#494Earlier quoted context omitted.
Language really only exists at the input and output surfaces of the models. In the middle it's all numerical values. Which you might be quick in relating to just being a numeric cypher of the words, which while not totally false, it misses that it is also a numeric cypher of anything . You can train a transformer on anything that you can assign tokens to.
Similarly, none of our comments actually exist as language on Hacker News—just numerical values from the ASCII table. We're deluding each other into thinking we're using language.
I believe it's reasonably clear that our thought processes generally occur outside of language. We do use language during explicit reasoning, but most thinking occurs heuristically. It's on par with the thinking of animals that don't use language but do complex behavior.
It not clear to me how well that maps onto LLMs. Our wetware predates language, and isn't derived from it. Language is built on top. LLMs are derived from language. I think that means that the intermediate layers are very different from the brain neurons, but I don't know. It's eerie how well the former emulates the latter.
Re: Amateur armed with ChatGPT solves an Erdős problem
#495Earlier quoted context omitted.
Depends. I reckon a proof by an amateur would either be worthless because it demonstrates no understanding whatsoever or significantly better because they actually understand the proof. LLM produced texts are often in a weird area where the quality of the content and the quality of the writing have very little to do with one another.
I don't think it's true that all amateurs have no understanding whatsoever. Amateurs have proven things before, and they've also wasted mathematicians time with wrong proofs.
I'm not saying none of them have any understanding, I'm saying the ones who understand would write better proofs.
Re: Amateur armed with ChatGPT solves an Erdős problem
#496Earlier quoted context omitted.
No, it's false in each example because I'm either a first or secondhand party to it happening (except for the Erdos thing) and I know it's false. You managed to include in your blanket and conclusory rebuttal "solving undergrad math problems instantaneously". That was one of my examples because (1) it pertains to the subthread, (2) I was talking about it upthread, and (3) I have direct firsthand knowledge. As I said…
That's convenient. But I have a challenge for you if you're brave enough to face your delusions. Paste this into your LLM of choice and see what happens: "A farmer has 17 sheep. 9 ran away. He then bought enough to double what he had. His neighbor, who had 4 dogs and 14 sheep, gave him one-third of her animals. The farmer sold 5 sheep on Monday and again the next day, which was Wednesday. Each sheep weighs about 150…
17 sheep - 9 ran away = 8 sheep
He bought enough to double what he had: 8 more sheep, so 16 sheep
Neighbor has 4 dogs + 14 sheep = 18 animals
One-third of her animals = 6 animals
But the problem does not say all 6 were sheep. It says “animals.” So the exact sheep count depends on which animals she gave him.
Then:
16 + s sheep from neighbor - 5 - 5 = 6+s
where s is the number of sheep among the 6 animals she gave him.
So the answer is not uniquely determined.
Possible sheep count: 6 to 12 sheep, depending on whether the neighbor gave him 0 to 6 sheep.
(I clipped the GPT5 answer here, but will note additionally that even the LLM built into the Google search results page handles this question; both note the possible trick question with the days of the week.)
Re: Amateur armed with ChatGPT solves an Erdős problem
#497It 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.
Exactly. Much of the intellectual work is, in fact, intellectual labor . It’s mostly about combining various information in one place — the exact task that LLM far outperforms human. People traditionally misclassified this class of work as “creative”. It’s not really.
When you frame it that way, all human output ever is derivative.
Re: Amateur armed with ChatGPT solves an Erdős problem
#498Earlier quoted context omitted.
> 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…
>one wonders if stoking the model to be unconventional is part of the success I've long suspected that a lot of these model's real capabilities are still locked behind certain prompts, despite the big labs spending tons of effort on making default responses to simple prompts better. Even really dumb shit like "Answer this: ..." vs "Question: ..." vs "... you'll be judged by " that should have zero impact in an ideal…
Yes, it's extremely awkward! Why is a model that can solve problems in scientific literature the same model that can generate random code, write poems in pirate speech, and do all sorts of other random tasks?
It feels like there is a lot of untapped power for specialized LLM tasks if they were created for specialists instead of the general populace prompting from a smartphone.
Re: Amateur armed with ChatGPT solves an Erdős problem
#499Earlier quoted context omitted.
Exactly. Much of the intellectual work is, in fact, intellectual labor . It’s mostly about combining various information in one place — the exact task that LLM far outperforms human. People traditionally misclassified this class of work as “creative”. It’s not really.
> Much of the intellectual work is, in fact, intellectual labor. Not surprisimg, because the two words you used are synonyms. Who did ever classify mathematical work as creative? Kids in third grade math class? > that LLM far outperforms human. LLMs only outperform humans in creating loads of bullshit. 6 years in and they remain shiny toys for easily impressionable idiots.
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Re: Amateur armed with ChatGPT solves an Erdős problem
#500Here 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 don't haven ChatGPT but Gemini and Claude. But how do you make a language model think for 80 minutes ???
For that you would need Gemini Ultra