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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

#461

Post by TMWNN »

progbits wrote: post #68
napoleoncomplex wrote: post #21

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.

From the prompt: > You should do a breakthrough This is just as funny and ridiculous as those "make no mistake" prompts.

The day is coming when some *BIG* problem is solved by AI just because someone jokingly asks about it.

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

#462

Post by TMWNN »

bredren wrote: post #209
ecshafer wrote: post #31

Terrance Tao's chatgpt conversation is really interesting for a variety of reasons: 1. The counter example wasn't just a brute force selection, the polynomial is structured in a very specific way that ends up getting the result. 2. Terry Tao's questions are very specific and prompts the AI in a useful way, that without high math training you are not going to get the same information out of it. Terry seems to see some…

It is ~a meme on subreddits that developers struggling to get good results out of any given model is a "skills issue." But I think your comment drives at some authentic take on this. Skill with AI is not only crafting iterative prompts the agent will understand, but also very high domain-specific knowledge of what the prompts explore. One without the other can result in frustration or worse.

>It is ~a meme on subreddits that developers struggling to get good results out of any given model is a "skills issue."

*GIT GUD* (at prompting)

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

#463

Post by ProllyInfamous »

Frost1x wrote: post #338
metanonsense wrote: post #315

Earlier quoted context omitted.

It feels very humbling that here is one of the smartest humans on the planet asking questions, and the LLM keeps answering in this "Yes, it's really simple if you think about it" way, like a professor talking to a talented student.

I had a similar reaction with the language but also response times and language. It reminded me of a quote about Jon von Neumann from Edward Teller: "Von Neumann would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us."

Von Neumann is an interesting historical character that nobody has ever heard of, e.g: for such an accomplished inventor, that so few minutes of video footage exist of him.

>I sometimes wondered if he used the same principle when he talked to the rest of us.

I can come pretty close to a humbler example of this, as the more-extroverted "bad twin," of an identical set: my own genetic equal is bored to tears interacting with 90% of daily interactions... we both started with good brains/IQ, then went to the same college; but while twin spent the next decades solving EE problems (and co-founding startups), I "kicked back" and smoked myself sillyretarded, electricianing, relying upon bullshit and sheer luck to get to where I [barely maintain] am.

Watching my twin deal with any normal-intelligence persons is such an unpredictable shitshow, but I pretty much always know he's "dealing with us toddlers" who mostly never grew up. His patience is limited but willing.

Glad he can get by among us mere mortals. I have other similarly-minded brothers, but only this one identical twin.

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

#464

Post by theplumber »

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.

Indeed that’s the case but most of the programming problems are solved problems and unless you care how things are done someone with less/no knowledge can still make great use of programming to do what it needs to do.

Let’s not pretend you need to be programmer to use AI for programming like mathematicians need to solve math problems. Programming (most of the time)solves real problems rather than abstract constructs.

AI is already good enough to create the next “Facebook”(v1 and maybe v2 as well) without any real programmer. This makes the AI a big enabler and reduces the need for programmers vastly in the early stages of any business.

That being said as more online businesses will flourish these will require actual programmers after they get enough traction so the debate is still on if it will lead to massive layoffs in our industry.

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

#465

Post by dwd »

jdw64 wrote: post #29

I'm watching how Tao uses AI, and it's interesting. Expand the entire expression, then change the representation to find the core axis. You can't see the axis from just one perspective, so you change the representation. In programming terms, it's like applying multiple domain models. Then break it down into small contract units. Why is it a Jacobian monomial? Why does x satisfy a cubic equation? And so on. Then swap…

Been doing something similar and I would add that playing multiple LLMs off on each other gets a far superior result.

One LLM would suggest a tightening of a particular axiom, and I would ask the rest what the consequences are: what is gained, what is lost and decide whether to use it. Often another would suggest a tweak that then goes back and a recursion.

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

#467

Post by [deleted] »

godelski wrote: post #427
napoleoncomplex wrote: post #21

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…

[deleted]

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

#468

Post by mvkel »

The most important prompt lesson everyone should take away: never ask yes / no / leading questions.

Almost all of Tao's questions begin with what, or why. That forces an open ended response, which is a great way to reduce or eliminate sycophancy and severe hallucinations. The less you steer, the more accurate it gets.

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

#469

Post by reverius42 »

aleph_minus_one wrote: post #417
agrounds wrote: post #380

Earlier quoted context omitted.

I studied a lot of abstract algebra in college and grad school and I’m surprised that rings and algebras would come up in a CS degree. What algorithms topics used those concepts? Something about polynomials?

Rings: * Determinant calculation: - The Samuelson–Berkowitz algorithm is best understood in terms of general rings - The Faddeev–LeVerrier algorithm and determinant calculation using Gaussian elimination work on rings with specific properties (for the Faddeev–LeVerrier algorithm the restriction is on the characteristic of the ring, for Gaussian elimination the ring must be an integral domain (ideally a field)). * Rin…

> The tropical semiring has various applications (see tropical analysis), and forms the basis of tropical geometry. The name tropical is a reference to the Hungarian-born computer scientist Imre Simon, so named because he lived and worked in Brazil.[1]

I'm convinced half the reason people find CS terminology more accessible and Math terminology less so, is that CS terminology tends to be named after stuff, and Math terminology tends to be named after people, and ... sometimes whether the place they lived is a tropical place.

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