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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

#261

Post by azan_ »

Eufrat wrote: post #172
dinkumthinkum wrote: post #99

Earlier quoted context omitted.

No meaningful, practical applications? You realize that sounds incredibly naive in the history of mathematics, right? People thought this way about number theory in general, and many other things that turned out to have quite important practical applications. Your statement is also a bit odd in that researchers are already paid throughout their whole careers to solve such problems. I don't know.

> You realize that sounds incredibly naive in the history of mathematics, right? This is after the fact justification. You are arguing that because a thing (number theory) showed practical applications we should have dumped a lot more effort into it. There is no basis for this argument whatsoever; it also seems to involve inventing a time machine. Number theory had no practical applications until the development of p…

> Number theory had no practical applications until the development of public-key cryptography, but you cannot make funding decisions based on the future since it’s unknowable.

You are completely missing the point. The point is that we should invest in pure maths because it has always been an investment with very good ROI. The funding should be focused on what experts believe will advance pure maths more (not whether we believe that in 100 years this specific area will find some application) and that's pretty much what we are doing right now. I think it's just your anti-AI sentiment that's clouding your judgement and since AI succeeded in proving pure maths results, you are inclined to downplay it by saying that well, pure maths is worthless anyway.

Re: Amateur armed with ChatGPT solves an Erdős problem

#263

Post by _0ffh »

resident423 wrote: post #91
thesmtsolver2 wrote: post #75

Earlier quoted context omitted.

Remember when people thought multiplying numbers, remembering a large number of facts, and being good at rote calculations was intelligence? Some people think that multiplying numbers, remembering a large number of facts, and being good at calculations is intelligence. Most intelligent people do not think that. Eventually, we will arrive at the same conclusion for what LLMs are doing now.

Remember when people thought solving Erdos problems required intelligence? Is there anything an LLM could ever do that would cound as intelligence? Surely the trend has to break at some point, if so what would be the thing that crosses the line to into real intelligence?

Well, the famous Turing test was evidently insufficient. All that happened is that the test is dead and nobody ever mentions it anymore. I'm not sure that any other test would fare any better once solved.

Re: Amateur armed with ChatGPT solves an Erdős problem

#264

Post by xxs »

noosphr wrote: post #102
resident423 wrote: post #91

Earlier quoted context omitted.

Remember when people thought solving Erdos problems required intelligence? Is there anything an LLM could ever do that would cound as intelligence? Surely the trend has to break at some point, if so what would be the thing that crosses the line to into real intelligence?

I've spend a good chunk of time formalising mathematics. Doing formalized mathematics is as intelligent as multiplying numbers together. The only reason why it's so hard now is that the standard notation is the equivalent of Roman numerals. When you start using a sane metalanguage, and not just augmrnted English, to do proofs you gain the same increase in capabilities as going from word equations to algebra.

>the standard notation is the equivalent of Roman numerals.

But the Roman numerals are easy. I was able to use them before 1st grade and I can't touch any "standard notation" to this day.

Re: Amateur armed with ChatGPT solves an Erdős problem

#265

Post by urutom »

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…

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 of watching the search itself, not just the final result.

Re: Amateur armed with ChatGPT solves an Erdős problem

#266

Post by DeathArrow »

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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#267

Post by throwaway198846 »

thesmtsolver2 wrote: post #135
resident423 wrote: post #91

Earlier quoted context omitted.

Remember when people thought solving Erdos problems required intelligence? Is there anything an LLM could ever do that would cound as intelligence? Surely the trend has to break at some point, if so what would be the thing that crosses the line to into real intelligence?

When will LLM folks realize that automated theorem provers have existed for decades and non-ML theorem provers have solved non-trivial Math problems tougher than this Erdos problem. Proposing and proving something like Gödel's theorem's definitely requires intelligence. Solving an already proposed problem is just crunching through a large search space.

Automated theorem provers can't prove this problem. Which non-trivial Math problem you think are thougher than this Erdos problem?

Re: Amateur armed with ChatGPT solves an Erdős problem

#268

Post by Vachyas »

liweic wrote: post #235
cryptoegorophy wrote: post #41

Earlier quoted context omitted.

Mine took 20min. Pro. https://chatgpt.com/share/69ed83b1-3704-8322-bcf2-322aa85d7a... But I wish I was math smart to know if it worked or not.

Wired enough, Pro+extended with the same prompt, just output directly without thinking: https://chatgpt.com/s/t_69edd2d9dc048191b1476db92c0dedf8 . Does this mean the result was cached or that it simply routes to a different model silently based on the user?

The link you provided is for a canvas I think rather than the convo

Re: Amateur armed with ChatGPT solves an Erdős problem

#269

Post by sunaookami »

bsza wrote: post #256
simianwords wrote: post #243

Earlier quoted context omitted.

what? the post is literally titled "Amateur armed with ChatGPT solves an Erdős problem". stop spreading FUD about unaffordability

They used ChatGPT Pro to solve it. Over 50% of people in the world couldn't afford ChatGPT Pro ($200/mo) even if they spent more than half of their income on it. [1] What was that about "spreading FUD about unaffordability"? [1] https://ourworldindata.org/grapher/share-living-with-less-th...

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.
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