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Amateur armed with ChatGPT solves an Erdős problem

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Re: Amateur armed with ChatGPT solves an Erdős problem

#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.)

Re: Amateur armed with ChatGPT solves an Erdős problem

#232
post #202

Earlier quoted context omitted.

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.

What is your idea of "creative"/"creativity" then?

Coming up with said novel techniques in the first place. Arguably something that most humans can't really do reliably or at all.

Re: Amateur armed with ChatGPT solves an Erdős problem

#233

Earlier quoted context omitted.

Proving a negative is a pretty high bar. You also have the problem of defining "real intelligence", which I suspect you can't.

Intelligence is Intelligence. It's intelligent because it does intelligent things. If someone feels the need to add a 'real' and 'fake' moniker to it so they can exclude the machine and make themselves feel better (or for whatever reason) then they are the one meant to be doing the defining, and to tell us how it can be tested for. If they can't, then there's no reason to pay attention to any of it. It's the equivale…

> It's intelligent because it does intelligent things.

Most people would consider someone who can calculate 56863*2446 instantly in their head to be intelligent. Does that mean pocket calculators are intelligent? The result is the same.

> then they are the one meant to be doing the defining, and to tell us how it can be tested for. If they can't, then there's no reason to pay attention to any of it.

That is the equivalent of responding to criticism with “can you do better?”. One does not need to be a chef (or even know how to cook) to know when food tastes foul. Similarly, one does not need to have a tight definition of “life” to say a dog is alive but a rock isn’t. Definitions evolve all the time when new information arises, and some (like “art”) we haven’t been able to pin down despite centuries of thinking about it.

Re: Amateur armed with ChatGPT solves an Erdős problem

#234

I will get downvoted for this but I can't help thinking that billions of dollars have gone into chatgpt over a period of years and an LLM can direct all its "attention" (in a metaphorical sense) on one problem. I think if you gave top mathematicians a few million (so a fraction of a percent of chatgpt budget) to solve this problem over four years, they probably would have at least made significant progress. I don't t…

[deleted]

Re: Amateur armed with ChatGPT solves an Erdős problem

#235

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…

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?

Re: Amateur armed with ChatGPT solves an Erdős problem

#236
post #171

Earlier quoted context omitted.

I don't have any opinion about "real intelligence" or not. I'm not a P(doom)er, I don't think we're on the bring of ascending as a species. But I'm also allergic to arguments like "they're just statistical text generators", because that truly does not capture what these things do or what their capabilities are.

Just to clarify because I’m not sure I understand: So you agree that LLMs are in fact statistical text generators but you don’t like people use that fact in arguments about the capabilities of the things?

It's like a genotype/phenotype distinction, the genotype may be statistical text generator but the phenotype is something much more.

Re: Amateur armed with ChatGPT solves an Erdős problem

#237

Earlier quoted context omitted.

None of it is really from logical thought. The rationalizations don't make any sense, but they haven't for a while. It's an emotional response. Honestly, It's to be expected.

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 technological progress equally. /s

Re: Amateur armed with ChatGPT solves an Erdős problem

#238
post #226

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? Hah. It reminds me of this great quote, from the '80s: > There is a related “Theorem” about progress in AI: once some mental function is programmed, people soon cease to consider it as an essential ingredient of “real thinking”. The ineluctable core of intelligence is a…

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 the key part of the quote, this is somehow not related to "intelligence". Something that 2 years ago was not possible (again, according to a leading expert in this field), is possible today. And yet this is somehow something that they always could do, and since they're doing it today, is suddenly no longer important. On to the next one!

No idea why this is related to darwin or definitions of life. The definitions don't change. What people considered important 2 years ago, is suddenly not important anymore. The only thing that changed is that today we can see that capability. Ergo, the quote holds.

Re: Amateur armed with ChatGPT solves an Erdős problem

#239

Earlier quoted context omitted.

None of it is really from logical thought. The rationalizations don't make any sense, but they haven't for a while. It's an emotional response. Honestly, It's to be expected.

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

Re: Amateur armed with ChatGPT solves an Erdős problem

#240
post #202

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.

I agree except: this is creative work. Creativity can be and is being mechanised. True originality is extremely rare. Most novelty is the repurposing of one idea or concept elsewhere in a way we call find surprising, but the choice to apply A to B could have been made for any reason including mechanical: very many inventions are accidents. In-depth knowledge / conceptual understanding of something is built on abstraction, and abstractions are portable.

If you had a list of N concepts and M ways to apply them you could try all N*M combinations, and get some very interesting results. For a real example, see the theory of inventive problem solving (TRIZ)'s amusing "40 principles of invention" by Soviet inventor Genrich Altshuller. https://en.wikipedia.org/wiki/TRIZ

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