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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

#571

Post by jgalt212 »

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.

My rule of thumb is: Never ask an LLM a question where you don't know what the right answer or wrong answer looks like.

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

#572

Post by tdeck »

jstummbillig wrote: post #523
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.

That is probably not going to be the important difference. You can't use it for theoretical physics because you have no meaningful question and there is no result that you can do anything with. In contrast you don't need to be a coder to understand if your to-do list for cats works: You have an idea of what you want. You know the rough shape of what an app is and what it can do. You can put it in front of your can an…

There are still some interesting pitfalls though. A friend of mine vibe coded a small browser based app to track something personal over a long time period. Eventually he plans to share the app with others. It worked, but I was curious where it stored the data and he didn't know.

It turned out it was using LocalStorage, which is not entirely unreasonable, but there are obvious drawbacks (e.g if you move the file it might become inaccessible, if you switch machines there's no convenient way to transfer the data, there are all kinds of ways to lose it, etc..).

In this case "how is this storing my data" is a fundamental question with plenty of implications for your app over its lifetime, but most non-computer people don't think to ask it at all. These days many users enter CS programs without knowing how to manage files and folders on their computer, because even that is often abstracted away.

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

#573

Post by dezsiszabi »

ProllyInfamous wrote: post #463
Frost1x wrote: post #338

Earlier quoted context omitted.

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 interactin…

I definitely heard of him. The CS focused high school I went to in Hungary was named after him, his portrait on the walls, etc.

I think lots of people have heard of him. I agree, that he is probably not as famous as some of the other scientists of the era though.

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

#574

Post by jvanderbot »

mohamedkoubaa wrote: post #295
jvanderbot wrote: post #26

It's crazy how he suggests simplifications over and over and gets led through the finding. Absolutely bonkers how you can use AI to understand something and map it to your own mental map so efficiently, and of course he's most interested in generalizing or finding a simpler sub-result that would explain it. Just awesome to see new knowledge hit an incredible mind like this. Having these "what if" discussions is what…

Hold on isn't this how math professors used grad students for hundreds of years?

"used" is a bit loaded, but this is just how people talk to eachother when they are thinking really hard about something they want to solve. So, I'm fairly sure it goes back as far as speech. It's just debugging - "What if it was caused by xyz", "What if we tried abc"

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

#575

Post by dnemmers »

satvikpendem wrote: post #503
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...

The paradox is analogous to AI poisoning its own training data as more and more AI generated content is released on the Internet. Indeed, I see a hard terminus for both man and machine at some point.

Absolutely right. First gen models are trained on 'virgin' non-LLM output. Subsequent models are tainted by ingesting AI replies. Rinse and repeat, and all you end up with is AI copies of AI replies, and the noise will completely overtake the signal.

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

#576

Post by inigyou »

david-gpu wrote: post #562
inigyou wrote: post #514

Earlier quoted context omitted.

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

[flagged]

I'm not seeing what this has to do with my point? It feels like an attempted gotcha, but without any gotcha?

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

#577

Post by sebmellen »

chongli wrote: post #299
sebmellen wrote: post #220

Earlier quoted context omitted.

For those of us with strong verbal processing and weak symbolic/pattern processing, this makes math much more difficult to approach. Interestingly, discrete math feels the most "verbal" of all the subfields of math I've encountered (I haven't gone very deep). I think this is because notation in discrete math is is somehow closer to compressed prose or logic, whereas other forms of math use notation to fill in for lon…

No, math is difficult to approach because it's genuinely deep . Trying to verbalize what is going on is extremely difficult, because you end up saying stuff like "and then do that to all of these things, and then do it again to all of the results, and so on ad infinitum, and then take the collection of all of that, and join it with the collection of doing the same procedure as before starting with a different set of…

Of course, I understand this, and I hope that my comment didn't come across as saying that math would be easier to "do" if it were all fully verbal. Symbolic reasoning and interpretation are necessary for complex reasoning.

And math is, as you know, a deep but traversable graph. The traversal inherently requires a familiarity with the nodes you pass through when reaching a foreign or more difficult concept.

However, I'll give you an example. If I read through more complex math that I’m not comfortable with in Sage, I can build an intuition for the structure of the problem more easily than if I view the “raw” notation. In that sense, it is easier to for me to “approach” — but approaching something is very different from fluently using it — and I’m under no illusion that approaching a topic is the same as beginning to understand it.

Again, this is definition-dependent. To me, “approaching” something means beginning to glean how I might one day understand it. E.g. watching a 3B1B video feels like “approaching” a topic. Here we reach the limits of language already :)

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

#578

Post by MeteorMarc »

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…

I think the questions are sufficiently suggestive to induce hallucinations. Still a lot of manual work to check all these claims.

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

#579

Post by Myrmornis »

dash2 wrote: post #521
WarmWash wrote: post #224

Earlier quoted context omitted.

> https://en.wikipedia.org/wiki/Transmission_Control_Protocol compare to > https://en.wikipedia.org/wiki/Rees_algebra Most people, especially non-tech technical people, could crash through the TCP article and come out the other side with at least a high level understanding of it. Most people, even technical ones, could not even get through the first line of the rees article, heck the first statement of the article. A…

Yeah, as a scientist I can read most Science or Nature articles in most fields, and get a rough idea. Not every piece of jargon, but I can understand roughly what they did, read the graphs and figure out the result. A friend sent me his maths PhD and I did not understand a single sentence .

That's not because the nomenclature is bad, it's because the concepts in advanced mathematics are further from our familiarity zone. In other words because it's hard.

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

#580

Post by mastermage »

v9v wrote: post #497
mastermage wrote: post #494

Earlier quoted context omitted.

Or in the words of Clickbait articles: MATHMATICIANS SHIVER OF THE IMPLICATIONS OF AI WILL MATHMATICIANS NO LONGER BE NEEDED. to which betteridge's law of headlines says: NO.

That law only applies to headlines ending in a question mark.

It is question i just foegot the Questionmark because i am dumb.
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