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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

#241

Post by hansmayer »

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.

> 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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#242

Post by simianwords »

missingdays wrote: post #239
threethirtytwo wrote: post #134

Earlier quoted context omitted.

It's because HN is not really full of smart people. It's full of people who think they're smart and take pride in that idea that they're pretty intelligent. ChatGPT equalizes intelligence. And that is an attack on their identity. It also exposes their ACTUAL intelligence which is to say most of HN is not too smart.

> 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

Re: Amateur armed with ChatGPT solves an Erdős problem

#243

Post by simianwords »

bsza wrote: post #237
threethirtytwo wrote: post #134

Earlier quoted context omitted.

It's because HN is not really full of smart people. It's full of people who think they're smart and take pride in that idea that they're pretty intelligent. ChatGPT equalizes intelligence. And that is an attack on their identity. It also exposes their ACTUAL intelligence which is to say most of HN is not too smart.

> ChatGPT equalizes intelligence Yes, I love living in communism too. Imagine if you had to pay money for it or something. The wealthiest people would get unrestricted access to intelligence while the poor none. And the people in the middle would eventually find themselves unable to function without a product they can no longer afford. Chilling, huh? Good thing humans are known for sharing in the benefits of technolo…

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

Re: Amateur armed with ChatGPT solves an Erdős problem

#244

Post by latexr »

NitpickLawyer wrote: post #238
latexr wrote: post #226

Earlier quoted context omitted.

That is a “gotcha” born of either ignorance (nothing wrong with that, we’re all ignorant of something) or bad faith. Definitions shift as we learn more. Darwin’s definition of life is not the same as Descartes’ or Plato’s or anyone in between or since because we learn and evolve our thinking. Are you also going to argue definitions of life before we even learned of microscopic or single cell organisms are correct and…

I don't see it as a gotcha. Just an (evergreen, it seems) observation that people will absolutely move the goalposts every time there's something new. And people can be ignorant outsiders or experts in that field as well. For example, ~2 years ago, an expert in ML publicly made this remark on stage: LLMs can't do math. Today they absolutely and obviously, can. Yet somehow it's not impressive anymore. Or, and this is…

> 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 remark on stage: LLMs can't do math. Today they absolutely and obviously, can.

How exactly are “LLMs can’t” and “do math” defined? As you described it, that sentence does not mean “will never be able to”, so there’s no contradiction. Furthermore, it continues to be true that you cannot trust LLMs on their own for basic arithmetic. They may e.g. call an external tool to do it, but pattern matching on text isn’t sufficient.

> The definitions don't change.

Of course they do, what are you talking about? Definitions change all the time with new information. That’s called science.

Re: Amateur armed with ChatGPT solves an Erdős problem

#245

Post by smallnamespace »

LeCompteSftware wrote: post #230
timjver wrote: post #224

Earlier quoted context omitted.

Verifying that every step in a (potentially long) proof is sound can of course be much, much harder than verifying that a definition is correct. That's kind of the whole point.

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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#246

Post by azan_ »

downboots wrote: post #211
dataflow wrote: post #168

Question for those who believe LLMs aren't intelligent and are merely statistical word predictors: how do you reconcile such achievements with that point of view? (To be clear: I'm not agreeing or disagreeing. I sometimes feel the same too. I'm just curious how others reconcile these.)

It doesn't matter if you use a car or go there walking. If your goal is cave exploration, the tools are irrelevant.

But in this specific case AI actually explored the cave for you. Comparing it to car getting you to the cave is really bad comparison.

Re: Amateur armed with ChatGPT solves an Erdős problem

#247

Post by [deleted] »

energy123 wrote: post #159
CSMastermind wrote: post #147

For the uninitiated, Paul Erdős was a pretty famous but very eccentric mathematician who lived for most of the 1900s. He had a habit of seeking out and documenting mathematical problems people were working on. The problems range in difficulty from "easy homework for a current undergrad in math" to "you're getting a Fields Medal if you can figure this out". There's nothing that really connects the problems other than…

> 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…

[deleted]

Re: Amateur armed with ChatGPT solves an Erdős problem

#248

Post by ngruhn »

cubefox wrote: post #231

Current headline: "An amateur just solved a 60-year-old math problem—by asking AI" A more honest title would be: "An AI just solved a 60-year-old math problem—after being asked by amateur" (Imagine the headline claimed instead that a professor just solved a math problem by asking a grad student.)

Previous problems solved by AI had some amount of expert guidance/steering. Here, I guess the emphasis is that there was none of that.

Re: Amateur armed with ChatGPT solves an Erdős problem

#249

Post by bonesss »

burnerRhodov2 wrote: post #225
sigmoid10 wrote: post #219

Earlier quoted context omitted.

>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…

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 lifespan, but: even the possibility to objectively map out some specific aspect of a regional approach to social rights in a given time period and consider it with another social framework, alongside automated & verifiable execution of policy, irrespective of the language of origin is incredible.

Instead of hundreds and thousands of incommensurate legislative silos we might create a bazaar of shared improvement and governance efficiency. Turnkey mature governance and anti-corruption measures for newborn nations and countries trying to break out of vicious historical exploitation cycles. Fingers crossed.

Re: Amateur armed with ChatGPT solves an Erdős problem

#250

Post by virgildotcodes »

nextaccountic wrote: post #194
manfromchina1 wrote: post #106

Earlier quoted context omitted.

Free ChatGPT is like a fast car with a barely responsive steering wheel. Guardrails on that thing are insane. Even for math. It wont let you think. It will try to fix mistakes you havent even made yet based on intent that was ascribed to you for no reason. It veers off in some crazy directions thinking that's what you meant and trying to address even a little bit of that creates almost a combinatorial explosion of ev…

So this doesn't happen in the paid plans of ChatGPT? But why?

Paid plans give you access to much larger, more intelligent models which have thinking enabled (inference time compute). In the example here you can see GPT Pro taking 20-80 minutes to respond with the proof.

All this is far more expensive to serve so it’s locked away behind paid plans.

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