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Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

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Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#531

Post by rkuodys »

larsfaye wrote: post #436
michaelchisari wrote: post #12

Earlier quoted context omitted.

It reinforces how to "learn AI" is to first master the problem domain. I can use AI for coding after decades of coding. I can't use it for theoretical physics because I can't evaluate the responses.

Correctamundo. That's EXACTLY what I just wrote about. And how we'll create the next generation of people who know how to evaluate responses when we're creating a generation of people who are increasingly reliant on LLMs to do the work makes for a strange paradox. https://larsfaye.com/articles/ai-coding-will-prevent-experti...

I am not sure if I'm ignorant or have too much self esteem, but in cases where domain is not my expertise I try to cross challenge using different models to get less-biased and hopefully more correct insights.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#532

Post by amelius »

michaelchisari wrote: post #12
lukebuehler wrote: post #8

It’s endlessly fascinating to read the AI transcript of an expert who _really_ knows how to cut to the chase. It just shows how much you can potentially squeeze out of these models. I’m also surprised to see that even Terrence Tao seems to use it in a way that resembles, in progression, how I use llms in my area of expertise (emphasis on progression and usage patterns, not absolute skill, obv I don’t match that): sho…

It reinforces how to "learn AI" is to first master the problem domain. I can use AI for coding after decades of coding. I can't use it for theoretical physics because I can't evaluate the responses.

But the AI can teach you to do theoretical physics, by guiding you through materials it selected for you, helping you with questions, etc.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#533

Post by amelius »

natsucks wrote: post #235
michaelchisari wrote: post #12

Earlier quoted context omitted.

It reinforces how to "learn AI" is to first master the problem domain. I can use AI for coding after decades of coding. I can't use it for theoretical physics because I can't evaluate the responses.

More and more the skill of being able to ask the right question seems critical to me, and I don't know how one can do that without deeper and deeper domain expertise.

Yes, but sometimes the right question is "do I know enough about this subject to be asking questions about it?"

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#534

Post by beng-nl »

rkuodys wrote: post #531
larsfaye wrote: post #436

Earlier quoted context omitted.

Correctamundo. That's EXACTLY what I just wrote about. And how we'll create the next generation of people who know how to evaluate responses when we're creating a generation of people who are increasingly reliant on LLMs to do the work makes for a strange paradox. https://larsfaye.com/articles/ai-coding-will-prevent-experti...

I am not sure if I'm ignorant or have too much self esteem, but in cases where domain is not my expertise I try to cross challenge using different models to get less-biased and hopefully more correct insights.

I’m not trying to be snarky, but.. I wouldn’t try to upgrade an answer from a stranger you can’t fully trust to an expert answer you can trust by asking more strangers who have all only read the same books and use the same system for summarizing the books.

Similarly, sometimes I have to manually validate the output of an ai tool, analyzed over a large text I can’t practically read and understand, and best way I’ve found is to ask the tool (or another ai) to ‘show your work,’ ie make it help me make the determination by showing places in the text I have to read to follow its reasoning. We can never trust another ai directly to assess the validity of another ai.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#535

Post by budsniffer952 »

jeef_berky wrote: post #499
larsfaye wrote: post #436

Earlier quoted context omitted.

Correctamundo. That's EXACTLY what I just wrote about. And how we'll create the next generation of people who know how to evaluate responses when we're creating a generation of people who are increasingly reliant on LLMs to do the work makes for a strange paradox. https://larsfaye.com/articles/ai-coding-will-prevent-experti...

It's so obvious to some and may never be considered by others. If someone asks about AI I tell them step 1 is ask it how to do something you know all about. Step 2 is consider everything else you ask will be that inaccurate.

[flagged]

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#536

Post by budsniffer952 »

case wrote: post #486
mkagenius wrote: post #485

Earlier quoted context omitted.

> I can't use it for theoretical physics because I can't evaluate the responses. I think pretty much the opposite. I can ask it to explain to me in ways I understand it. Even drill down the simplest of equations. Since llms have infinite patience. All I need to learn anything is patience.

I think the issue is that LLMs can be so confidently and convincingly wrong about anything. And if we (LLM tool operators) don’t know the subject matter in question, we can’t easily distinguish what they are right or wrong about.

While humans are infallible and correct.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#537

Post by tempfile »

mkagenius wrote: post #491
case wrote: post #486

Earlier quoted context omitted.

I think the issue is that LLMs can be so confidently and convincingly wrong about anything. And if we (LLM tool operators) don’t know the subject matter in question, we can’t easily distinguish what they are right or wrong about.

They are solving jacobian conjectures, I don't think they will hallucinate till masters level of any subject. Edit: do give counter examples if you have any in maths, physics, chemistry, biology etc

This deduction is baseless, there is no reason to think an LLM will only hallucinate on complex topics. They still get the "number of es in seventeen" question wrong regularly. The kind of mistakes an LLM makes has no clear resemblance to the kind of mistakes a human makes, because they are not doing the same thing.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#538

Post by budsniffer952 »

tty456 wrote: post #511
michaelchisari wrote: post #12

Earlier quoted context omitted.

It reinforces how to "learn AI" is to first master the problem domain. I can use AI for coding after decades of coding. I can't use it for theoretical physics because I can't evaluate the responses.

But someone who is not well versed in coding can evaluate the output simply by running the built app and testing it, which is an oversimplification and omits the tech debt and eventual issues that an experienced developer would catch or restrict the output.

Ah, yes, "experienced developers" see all the problems and resolve all the tech debt preemptively, which is why the state of software (even pre-LLM) was so great.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#539

Post by renyicircle »

zkmon wrote: post #466

I'm not a mathematician. Could someone let me know, what's the objective of this conversation and what was the result?

The background is that a counterexample to a famous mathematical conjecture was recently posted on X by an Anthropic employee. The counterexample, in form of a polynomial, is easy to validate by doing simple calculations, but it's not clear why it works and why it is the way it is, from a deeper mathematical perspective. Specifically, the properties of the polynomial suggest that it's not just an accidental finding but has some involved geometric construction behind it. This is what Terry Tao's conversation with ChatGPT starts with: "does this polynomial have any symmetry or structure that makes the counterexample seem less miraculous?". Using the counterexample, work backwards to get the intuition behind it so that it can be constructed by an explicit procedure rather than taken out of thin air. The result is his blog post, discussed here: https://news.ycombinator.com/item?id=48998362

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#540

Post by tempfile »

retrochameleon wrote: post #300
singularity2001 wrote: post #249

Earlier quoted context omitted.

They will have decades of experience with AI and they will be able to guide them by sniffing their hallucinations from single words.

Hopefully in decades hallucinations will be largely solved.

Hallucinations are an essential feature of the technology, they cannot be "solved". You may as well hope that we solve the halting problem.
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