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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

#281

Post by bsza »

sunaookami wrote: post #269
bsza wrote: post #256

Earlier quoted context omitted.

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.

> 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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#283

Post by squidbeak »

jdub wrote: post #156
freakynit wrote: post #146

Earlier quoted context omitted.

This is what I personally consider as "reasoning" ... knowledge generalization and application across domains.

Less reasoning than a dimension of brute force unfamiliar to human brains.

Trying to diminish this as brute force (something by the way that is categorically not 'unfamiliar to human brains' - as anyone who has every worked on complex slippery problems will tell you) is foolish, when the models hypothesize along the way to their solutions. That's reasoning.

Re: Amateur armed with ChatGPT solves an Erdős problem

#284

Post by squidbeak »

pelasaco wrote: post #255
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.

accuracy and creativity are often quite difficult to achieve at the same time. Looks like LLM can do it, even though one can question how creative it really is...

Can one? It's surpassed the creativity of humans in this one problem at least.

Re: Amateur armed with ChatGPT solves an Erdős problem

#285

Post by muzani »

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…

They're tuned to target a certain customer demographic solving for certain problems. I've seen standard AI models to absolutely brilliant things sometimes. But the prompts to get it to perform like it did with GPT-3 seem to get lengthier and lengthier in time. At some point we'll probably just snip out smaller, specialized models to do certain things.

Re: Amateur armed with ChatGPT solves an Erdős problem

#286

Post by azan_ »

komali2 wrote: post #279
azan_ wrote: post #253

Earlier quoted context omitted.

> Capitalism already is a poor allocator of human effort, resources, and energy, why lock in on this specifically? It's absolutely best allocator of human effort there is. It has some problems but compared to alternatives it's almost perfect.

Looking around, the evidence doesn't seem to support this conclusion. 50% of food thrown away, yet people go hungry. Every privatized industry diminishes in quality and reach. Selects and optimizes for profit rather than for human need.

> 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 ones you'd never want to live in such as North Korea or Cuba (funny thing - even China urged Cuba to free their markets).

Re: Amateur armed with ChatGPT solves an Erdős problem

#287

Post by dalmo3 »

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…

Ah, yes, 2001 but on land.

Re: Amateur armed with ChatGPT solves an Erdős problem

#288

Post by brandensilva »

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.

Also curious about this, it seems like it would be important to guide these tools more specifically based on the domain of expertise.

Re: Amateur armed with ChatGPT solves an Erdős problem

#289

Post by latexr »

NitpickLawyer wrote: post #252
latexr wrote: post #244

Earlier quoted context omitted.

> For example, ~2 years ago, an expert in ML See, that’s a poor argument already. Anyone could counter that with other experts in ML publicly making remarks that AI would have replaced 80% of the work force or cured multiple diseases by now, which obviously hasn’t happened. That’s about as good an argument as when people countered NFT critics by citing how Clifford Stoll said the internet was a fad. > made this remar…

The definition of "can/cannot do math" didn't change. That's not up for debate. 2 years ago they couldn't solve an erdos problem (people have tried, Tao has tried ~1 year ago). Today they can. Definitions don't change. The idea that now that they can it's no longer intelligence is changing. And that's literally moving the goalposts. Read the thread here, go to the bottom part. There are zillions of comments saying th…

> The definition of "can/cannot do math" didn't change. That's not up for debate.

That is not the argument. The point is that the way you phrased it is ambiguous. “Math” isn’t a single thing, and “cannot” can either mean “cannot yet” or “cannot ever”. I don’t know what the “expert” said since you haven’t provided that information, I’m directly asking you to clarify the meaning of their words (better yet, link to them so we can properly arrive at a consensus).

> Definitions don't change.

Yes they do! All the time!

https://www.merriam-webster.com/wordplay/words-that-used-to-...

> And that's literally moving the goalposts.

Good example. There are no literal goal posts here to be moved. But with the new accepted definition of the words, that’s OK.

> There are zillions of comments saying this.

Saying what, exactly? Please be clear, you keep being ambiguous. The thread barely crossed a couple of hundred comments as of now, there are not “zillions” of comments in agreement of anything.

> You are keen to not trying to understand what the quote is saying. (…) If you can't or won't see that, there's no reason to continue this thread.

Indeed, if you ascribe wrong motivations and put a wall before understanding what someone is arguing, there is indeed no reason to continue the thread. The only wrong part of your assessment is who is doing the thing you’re complaining about.

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