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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

#561

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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.

Succinctly put by Pablo Picasso's remark: "Computers are useless. They can only give you answers".

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

#562

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if people use it to make money, does this not mean that they providing some sort of service which is valued and hence it improves lifes?!

No, money and value have been decorrelated for a long time. At least 5 years and arguably since Reagan.

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

#563

This is the second ChatGPT shared conversation I've seen today that is truly fascinating. The first one was someone proving another conjecture false by just repeatedly saying "keep going" to ChatGPT: https://x.com/DmitryRybin1/status/2079904005652893709 What a world we live in.

> What a world we live in. It's a really interesting world. You can spam GPT to get novel math results but here I am trying to scroll up to the beginning of the conversation and 5 minutes in I still don't know if I'm near the top yet. Scroll... wait for render... scroll... wait for render... repeat... We live in a world where there's so much crazy technology but few people use it to make products better or to improve…

On my mac if you scroll slightly a blob appears on a slider on the right and you slide it to the top to go to the top. I'm not sure about these hidden user interface features that you only find through trial and error.

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

#564

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> What a world we live in. It's a really interesting world. You can spam GPT to get novel math results but here I am trying to scroll up to the beginning of the conversation and 5 minutes in I still don't know if I'm near the top yet. Scroll... wait for render... scroll... wait for render... repeat... We live in a world where there's so much crazy technology but few people use it to make products better or to improve…

And I am still waiting for the Apple Reminders AI to sort Milk in the right category…

And meanwhile, I gave up trying to connect to my offices printer months ago. Paper free environment over here, planned or not.

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

#565

Earlier quoted context omitted.

No, money and value have been decorrelated for a long time. At least 5 years and arguably since Reagan.

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Decorrolated, not unrelated. It can provide value for some things, but not for others

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

#566

Jeez. While I obviously can't talk at all about the math, I've noticed a few things: a) The model thinks on some questions while straight answers on others. (I wish I'd knew from the questions if this is somehow correlated to hard tasks or "inventive" tasks, but that's way out of my league). b) The model sometimes pushes back. Again, I'd wish I knew if it was warranted, but I counted 2 instances where it said "yes, b…

The "yes, with caveats" thing is boilerplate for both Codex and Claude since this current generation. It's actually a bit annoying because it primes you to think that the caveats are real, but most of the time it's just something terribly obvious and not a real caveat, but the model probably has some system prompt that tells it to always consider caveats or something like that. Same as the model starting every reply…

This has to be one of the more annoying characteristics of the recent models.

Every answer is met with "But did you think about X", or "One more thing to consider" and it almost starts to feel manic as you dig down that hole.

Multiple times I've had to literally say "Stop with the follow-ups and suggestions. Just answer the questions clearly".

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

#567

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I encountered something fairly similar working with Claude a few days ago. For a current project I've been fairly hand-wavy with requirements since I was getting good results, but it seemed to be failing hard on some key points, so I started to be more strict with it. Even after the fails were resolved, I've noticed that Claude now behaves differently within that project, carefully checking and rechecking things up f…

The most powerful way to use Fable in particular seems to be to pit it against Sol as a reviewer (or, I suppose, vice versa.) After going back and forth a half-dozen times, the result tends to be pretty much bulletproof. What's somewhat disturbing is just how much Fable's code really does benefit from the review. It tends to leave a lot of low-hanging fruit, and you can see it getting kind of impatient when repeatedl…

The problem with that approach, the code becomes over-complex, over-engineered and more often than not, it will take a specific point and iterate over it.

It's still what I do 90% of the case until I feel it's good enough for my usage.

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

#568

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Yeah that's pretty much what gwern argues here[0]. Or to adapt another proverb: to predict the next token you first need to model the universe. [0] https://gwern.net/scaling-hypothesis#gwern-difference--effic...

> to predict the next token you first need to model the universe Exactly. The "most likely next" series of tokens, for example, when given the first half of a correct mathematical proof, is the correct rest of the proof. I have never seen anyone define "most likely next token" in such a way that this isn't true.

It's like saying that thinking cannot generate new knowledge because all thought is just rearranging the information we get from our senses, or memory of previous information from our senses, and we do nothing more than figure out the most likely word to say next in a conversation.

Either humans are not capable of intelligence or computers are capable of becoming intelligent. Neither or both.

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

#569

What was most remarkable to me from this transcript, was how strong of an equal the AI agent comes across compared to the user (Tao). And Tao is one of the top mathematicians of modern times. Yes, Tao is guiding it to where he wants to go. But also, Tao is actively learning from it and relying on its explaining, analysis, and inference abilities. You can easily imagine this conversation having taken place between Tao…

I find it helpful to think of LLMs as reflections. If you can talk like an expert mathematician at the model it will respond like one. While Terrance's first prompt looks trivial I expect a first year Uni student would be hard pressed to provide something that good. I guess it is kind of the inverse of the "you are an expert mathematician" prompt engineering of gpt3.5. Since no one ever says that to an expert mathema…

Isn't LLM doing something like argmax{x} P(x|context) where x is the next word, and context is the words before including your instructions? Thus, the LLM output is heavily depending on your instructions, and if you input an expert context it would produce an expert result. Consequently, domain expertise has a significant bearing on what you can achieve from LLM.

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

#570

Earlier quoted context omitted.

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.

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GP is saying that when you use it in a domain where you're familiar, you'll naturally spot bad or lazy approaches and heavily steer the LLM, so you should keep that in mind when using it in domains you aren't an expert in (and thus can't as easily spot those things). I'm not sure why the tone of your reply is so uncharitable.
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