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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

#291

Post by squidbeak »

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.

As I understand it, models form connections (weak or strong) between everything in their training sets, even the smallest details. They've already made other breakthroughs directly because of this ability and this line of research is likely to be incredibly fruitful.

Re: Amateur armed with ChatGPT solves an Erdős problem

#292

Post by aaron695 »

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.

[dead]

Re: Amateur armed with ChatGPT solves an Erdős problem

#293

Post by simianwords »

bsza wrote: post #281
sunaookami wrote: post #269

Earlier quoted context omitted.

They didn't buy ChatGPT Pro themselves. You could've done the same as the students in the article and get a free subscription if you were interested in this instead of trolling.

> You could've done the same Please show me the steps to get a $200 subscription for free that works 100% of the time regardless of who you are. I'm listening.

ChatGPT flattened the difference between top .0001 percentile mathematician and an amateur. This is the definition of making intelligence more available.

You are exaggerating the situation by essentially claiming since some people can’t afford 200 dollars this means ChatGPT is not democratising intelligence. It’s a bit strange to claim this because according to you it only becomes affordable when maximal number of people can afford it. It’s a bit childish.

Directionally it is democratising. Are more people able to afford higher level intelligence? Yes.

Re: Amateur armed with ChatGPT solves an Erdős problem

#294

Post by sfdlkj3jk342a »

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…

When using the web interface for ChatGPT like this, is there any way to tell which model is actually being used?

Re: Amateur armed with ChatGPT solves an Erdős problem

#295

Post by amelius »

DeathArrow wrote: post #266
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…

>don't search the internet. I think this was key. Otherwise the LLM could think it can't be done.

But it was trained on the internet.

Re: Amateur armed with ChatGPT solves an Erdős problem

#296

Post by omcnoe »

sigmoid10 wrote: post #219
energy123 wrote: post #159

Earlier 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…

Model output reflects on your input, and the effect is self reinforcing over the course of a whole conversation. Color you add around a problem influences the model behavior.

A "dumber"/vague framing will get a less insightful solution, or possibly no solution at all.

I don't even necessarily think this is a critical flaw - in general it's just the model tuning it's responses to your style of prompt. People utilize LLMs for all kinds of different tasks, and the "modes of thought" for responding to an Erdos problem versus software engineering versus a more human/soft skills topic are all very different. I think the "prompt sensitivity" issue is just coming bundled along with this general behavior.

Re: Amateur armed with ChatGPT solves an Erdős problem

#297

Post by pontifier »

teiferer wrote: post #198
Tarq0n wrote: post #174

Earlier quoted context omitted.

Not definitively. LLMs are stochastic with respect to input, temperature and the exact prompt. It's possible that the model was already capable of it but never received the exact right conditions to produce this output.

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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#298

Post by JumpCrisscross »

simianwords wrote: post #242
missingdays wrote: post #239

Earlier quoted context omitted.

> ChatGPT equalizes intelligence Citation needed

how can you ask this question with on a post titled "Amateur armed with ChatGPT solves an Erdős problem"???? are you looking for some randomised control trial? omg

Idk, going out on a limb and guessing the folks who hang out on erdosproblems.com aren’t run-of-the-mill dumbasses. The prompt, if you look at it, is actually quite clever. Not as clever as the proof. But far from the equalization OP posits.

Re: Amateur armed with ChatGPT solves an Erdős problem

#299

Post by LeCompteSftware »

smallnamespace wrote: post #245
LeCompteSftware wrote: post #230

Earlier quoted context omitted.

That's not what the parent comment meant. They meant checking the Lean-language definitions actually match the mathematical English ones, and that the Lean theorems match the ones in the paper. If that's true then you don't actually need to check the proofs. But you absolutely need to check the definitions, and you can't really do that without sufficient mathematical maturity.

Yes, and the child comment’s point is that formalizing the problem is likely easier than having the LLM verify that each step of a long deduction is correct, which is why Lean might be helpful.

But both of you are ignoring the parent comment! Actually you're ignoring the context of the thread.

Originally someone said "I wish I was math smart to know if [this vibe-mathematics proof] worked or not." They did NOT say "I'd like to check but I am too lazy." Suggesting "ask it to formalize it in Lean" is useless if you're not mathematically mature enough to understand the proof, since that means you're not mathematically mature enough to understand how to formalize the problem.

Then "likely easier" is a moot point. A Lean program you're not knowledgeable enough to sanity-check is precisely as useless as a math proof you're not knowledgeable enough to read.

Re: Amateur armed with ChatGPT solves an Erdős problem

#300

Post by simianwords »

JumpCrisscross wrote: post #298
simianwords wrote: post #242

Earlier quoted context omitted.

how can you ask this question with on a post titled "Amateur armed with ChatGPT solves an Erdős problem"???? are you looking for some randomised control trial? omg

Idk, going out on a limb and guessing the folks who hang out on erdosproblems.com aren’t run-of-the-mill dumbasses. The prompt, if you look at it, is actually quite clever. Not as clever as the proof. But far from the equalization OP posits.

Directionally it is correct - an amateur wouldn’t be able to do this without ChatGPT. You can’t expect maximal democratisation
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