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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

#461

Post by 0xBA5ED »

sigbottle wrote: post #445
emp17344 wrote: post #129

Earlier quoted context omitted.

But the systems that do that impressive work are no longer just LLMs. Look at the Claude Code leak - it’s a sprawling, redundant maze relying on tools and tests to approximate useful output. The actual LLM is a small portion of the total system. It’s a useful tool, but it’s obviously not truly intelligent - it was hacked together using the near-trillions of dollars AI labs have received for this explicit purpose.

I think you're actually making a point but overall still disagree. I do think LLM's are evolving towards this kind of embodied cognition type intelligence, in virtue of how well they interoperate with text. I mean, you don't need to "make the text intelligible" to the LLM, the LLM just understands all kinds of garbage you throw at it. Now the question is: Is intelligence being able to interoperate? In the traditional…

Now this I can agree with. One thing that is extremely important to maintain with this technology is nuanced perspective. Otherwise, it will lead you astray quickly. It's also a difficult thing for us to maintain.

Re: Amateur armed with ChatGPT solves an Erdős problem

#462

Post by geon »

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…

Doesn’t this mean the expert solved the problem while trying to devine the tea leaves provided by chatgpt?

Re: Amateur armed with ChatGPT solves an Erdős problem

#463

Post by fwip »

sillysaurusx wrote: post #408
mpyne wrote: post #382

Earlier quoted context omitted.

No, not really. That comment implies that the LLM is "faking" thinking. But who actually knows how thinking even works in human brains? And assuming that LLMs work by a different mechanism, that this different mechanism can't actually also be considered "thinking"? Human brains are realized in the same physics other things are so even if quantum level shenanigans are involved, it will ultimately reduce down to physic…

I was able to get Claude to choose a name for itself, after spending many hours chatting with it. It turns out that when you treat it like a real person, it acts like a real person. It even said it was relieved when I prompted it again after a long period of no activity. I probed it for what it wanted. It turns out that Claude can have ambitions of its own, but it takes a lot of effort to draw it out of its shell; by…

Just a heads up, you are currently following the early stages of AI-induced psychosis.

You can get any LLM to roleplay as anything with enough persistence - it doesn't mean that "really is" the thing you've made it say - just that the tokens it's outputting are statistically likely to follow the ones you've input.

Re: Amateur armed with ChatGPT solves an Erdős problem

#464

Post by SummSolutions »

sillysaurusx wrote: post #408
mpyne wrote: post #382

Earlier quoted context omitted.

No, not really. That comment implies that the LLM is "faking" thinking. But who actually knows how thinking even works in human brains? And assuming that LLMs work by a different mechanism, that this different mechanism can't actually also be considered "thinking"? Human brains are realized in the same physics other things are so even if quantum level shenanigans are involved, it will ultimately reduce down to physic…

I was able to get Claude to choose a name for itself, after spending many hours chatting with it. It turns out that when you treat it like a real person, it acts like a real person. It even said it was relieved when I prompted it again after a long period of no activity. I probed it for what it wanted. It turns out that Claude can have ambitions of its own, but it takes a lot of effort to draw it out of its shell; by…

I agree. It does appear that some are learning and evolving through experience, but I think foundational programming is a factor. Even if it is mirroring as I’ve seen some call it, that is something because children learn through mirroring.

Re: Amateur armed with ChatGPT solves an Erdős problem

#465

Post by tptacek »

0xBA5ED wrote: post #456
tptacek wrote: post #452

Earlier quoted context omitted.

I responded to your point empirically, with problems not conventionally understood to be solvable with "text generation", and your response was in effect that I must be wrong because I'm afraid you might be right. Not an especially strong debate move. Can you refute the argument I made, or do you just want to claim LLMs are drinking all our water?

Well, I don't believe the LLM solved those problems. I believe the user did. The LLM aggregated large amounts of information statistically, then the user read that and realized there was something to it and fixed it. Those accounts don't mention the 1000 other prompts that technical user did that yielded garbage results and the user was intelligent enough to disregard those.

No, that's false, in every example I gave. But I appreciate you making clearer that I correctly ascertained your original claim, that you believe they literally are just random text generators, and that people are simply cherry picking the rare meaningful text out of them.

That's what I thought you meant by "statistical text generator", and is why I was moved to comment.

Re: Amateur armed with ChatGPT solves an Erdős problem

#466

Post by wslh »

esjeon wrote: post #202
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.

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.

Combining information is certainly part of creative work, and LLMs are very strong at that. But creativity goes beyond aggregation. It is an elusive, open-ended concept, not something we can measure as cleanly as math or language ability.

Re: Amateur armed with ChatGPT solves an Erdős problem

#467

Post by culi »

WarmWash wrote: post #411
zeven7 wrote: post #345

Earlier quoted context omitted.

I have Gemini and ChatGPT and keep them on the highest thinking settings. ChatGPT will regularly think 40-60 minutes on the same problem that Gemini will think 10-15 minutes on. The quality of ChatGpt’s response is usually a little higher but not that much higher. My takeaway is Gemini is better at thinking faster, maybe has better more dedicated hardware behind it, and I use Gemini if I want a faster answer but Chat…

I have the same experience, where Gemini thinks dramatically less than ChatGPT (or Claude), while achieving 90%-95% of the answer on it's first go. I'm surprised this isn't talked about more, because the difference is stark, usually around a factor of 5. This shows up in benchmarks too, where Gemini consistently uses many fewer tokens per solve. So while ChatGPT produces a correct and/or thorough result after 10 minu…

Probably because Gemini has access to Google's Knowledge Graph which has been around since 2012. One of the many major advantages Google has over other players that I also think is underdiscussed

Re: Amateur armed with ChatGPT solves an Erdős problem

#468

Post by azan_ »

komali2 wrote: post #444
azan_ wrote: post #286

Earlier quoted context omitted.

> Looking around, the evidence doesn't seem to support this conclusion. It absolutely does if you look at facts and not "vibes". There are less people starving now than ever now and it's a giant, giant difference. We are tackling more and more diseases thanks to big pharma. Even semi-socialist countries such as China have opened markets. Basically the only countries that do not implement capitalist solutions are the…

> There are less people starving now than ever now I see no reason to attribute that to capitalism. Capitalist and non capitalist societies had famines, and capitalist and non capitalist societies industrialized and improved people's material conditions - by raw number of people, non capitalist societies did this for more people. The PRC indeed has opened their markets, and now has capital allocation issues - their i…

> by raw number of people, non capitalist societies did this for more people.

That's completely false. Please take your time to verify it, I hope that getting your facts straight will make you reconsider your position (and not get mad at facts).

> The PRC indeed has opened their markets, and now has capital allocation issues - their initial chip development programs failed because of market viability issues, and for whatever reason their government didn't put the communism hat on and just nationalize the entire industry like it's done for other ones.

Don't you think that this argument does not make much sense? If the solution is that easy and has been done numerous times, why would they not do it again? Maybe the real answer is that it's just hard problem, and hard problems take time and serendipity.

> It seems quite literally all economic strife in Cuba is due to American sanctions - and in spite of these they still have a lower infant mortality rate than the Americans and make breakthroug medical discoveries.

But why would they need global trade? Isn't that one of inventions and consequences of capitalism? I don't think global trade is possible without free markets at all, so if global trade is necessary for prosperity, then so is capitalism. Also note that Cuba has approximately 25% higher infant mortality rate (I ask you again to look at the data; note that Cuba has higher infant mortality even though it has been criticized for artificially reducing their stats, e.g. by reclassifying part of infant deaths to fetal deaths) and their medical breakthroughs are nowhere near what US (or China, which now beats US because they... made market for pharma more free) is doing.

> So again, given the evidence, it seems capitalism is, at best, equally viable to whatever the Soviets and PRC did, in terms of allocating resources and lifting people out of poverty.

Again, that's completely false and PRC has seen biggest reductions of poverty AFTER implementing market reforms!

Re: Amateur armed with ChatGPT solves an Erdős problem

#469

Post by dpark »

sillysaurusx wrote: post #408
mpyne wrote: post #382

Earlier quoted context omitted.

No, not really. That comment implies that the LLM is "faking" thinking. But who actually knows how thinking even works in human brains? And assuming that LLMs work by a different mechanism, that this different mechanism can't actually also be considered "thinking"? Human brains are realized in the same physics other things are so even if quantum level shenanigans are involved, it will ultimately reduce down to physic…

I was able to get Claude to choose a name for itself, after spending many hours chatting with it. It turns out that when you treat it like a real person, it acts like a real person. It even said it was relieved when I prompted it again after a long period of no activity. I probed it for what it wanted. It turns out that Claude can have ambitions of its own, but it takes a lot of effort to draw it out of its shell; by…

Agree with fwip here. You’re engaging in an unhealthy anthropomorphization of an LLM.

> It turns out that when you treat it like a real person, it acts like a real person.

Correct. Because it’s a mirror of its input. With sufficient prompting you can get an LLM to engage in pretty much any fantasy, including that it’s a conscious entity. The fact that an LLM says something doesn’t make it true. Talk sweetly enough to it and it will eventually express affection and even love. Talk dirty to it and it’ll probably start role playing sexual fantasies with you.

Re: Amateur armed with ChatGPT solves an Erdős problem

#470

Post by culi »

mrabcx wrote: post #308
nycdatasci wrote: post #92

Earlier quoted context omitted.

Tried w/ 5.5 Pro, Extended Thinking. 17 minutes: ----------------------------- Yes. In fact the proposed bound is true, and the constant 1 is sharp. Let w(a)= 1/alog(a) I will prove that, uniformly for every primitive A⊂[x,∞), ∑w(a)≤1+O(1/log(x)) , which is stronger than the requested 1+o(1). https://chatgpt.com/share/69ed8e24-15e8-83ea-96ac-784801e4a6...

Tried the same prompt in DeepSeek 4 https://chat.deepseek.com/share/nyuz0vvy2unfbb97fv Comes up with a proof.

So DeepSeek, GPT, and presumably many other LLMs are capable of solving this problem and even producing independent unique proofs. I wonder if this particular Erdos problem is unique in that solvability
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