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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

#581

Post by OGWhales »

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.

Gell-Mann Amnesia effect

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

#582

Post by StilesCrisis »

jameshart wrote: post #412
com2kid wrote: post #389

Earlier quoted context omitted.

A byte is quite real. On old machines you could open them up and literally point to where bytes were physically stored in memory. Now days of course the chips are small so you have to point to where the multiple gigabyte chips are at. But they are still quite physically. Heck a C pointer points to an actual physical location on your machine, if you ignore the MMU.

Wow and TCP sends a stream of those microscopic memory cells?

It sends electricity or radio waves, yeah? The bits aren't the cells, they are the electricity within the cells.

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

#584

Post by ryangittins »

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…

Well said! After a few years of LLM sycophancy convincing laypeople they've managed to make progress on or fully crack famous math problems it's satisfying to see a world-class mathematician really put it through its paces. It's all the more impressive that Tao seems satisfied with the conversation.

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

#585

Post by Myrmornis »

daynthelife wrote: post #508
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…

As mathematician, I actually agree. We could do a lot more to communicate ideas in a way non-experts can understand. For instance, most people are familiar with polynomials. Take a polynomial in x (with integer coefficients) and substitute x for 5t everywhere. So for instance, 2x^3 - 8x + 3 becomes 250t^3 - 40t + 3. The Rees algebra Z[5t] (here Z is the integers) is then just the set of all polynomials you can get th…

I'm sure you're right that there's poor terminology, and Wikipedia math is certainly daunting. But in general the many mathematical exposition PDFs scattered across the Internet are beautifully written by careful, intelligent people. I'm a software engineer who's spent many hours reading them and also trying to do graduate classes as an adult. It's unfortunately common on Hacker News to encounter people who think that "I'd be good at math if only they used code to explain it" or "I'd be good at math if it used better terminology/notation".

The truth is that math is hard: few other subjects have anything close to its crazy conceptual breadth and depth, with hardish concepts being built upon hardish concepts in many layers.

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

#586

Post by tdu01 »

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…

Pretty spot on

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

#587

Post by StilesCrisis »

aleph_minus_one wrote: post #549
versteegen wrote: post #409

Earlier quoted context omitted.

Having studied CS and maths to post-grad, I think you exaggerate. Although a CS course might use these tools, they didn't in my experience go into explaining or defining them. The only use of linear algebra I can remember was in analysis of recurrence relations for algorithms, and for some graph theory. And I had one CS course on multivariate generating functions (formal variables) but most CS students would have bee…

> Having studied CS and maths to post-grad, I think you exaggerate. Although a CS course might use these tools, they didn't in my experience go into explaining or defining them. I studied computer science (and mathematics) in Germany. I am very certain that this was taught to computer science students, even though (compared to the lectures for math students) the lecturer did not get very deep into these topics. > mos…

Do you think weed-out courses are a good thing? If these courses are so important, they should be taught in a way that students can understand. If they made it to college, and can program, they're clearly smart and motivated.

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

#588

Post by dnemmers »

mkagenius wrote: post #547
tempfile wrote: post #537

Earlier quoted context omitted.

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.

Specific quirk of llms, also pretty much solved by existing thinking models. I think you guys are misunderstanding me, you can still talk to a llm to learn everything about physics or maths.

The problem is that you have no idea of what you're being taught is actually correct.

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

#589

Post by mkl »

slartibardfast0 wrote: post #196
elviejo wrote: post #100

Earlier quoted context omitted.

That is why Iverson invented APL. As a notation to get rid of all those inconsistencies in math notation. And for years he taught math classes with APL on the blackboard without computers. whether he succeeded, is debatable. But APL is definitely powerful, succinct and "regular". In APL you don't infer the operation from the types at all. × is elementwise, +.× is inner product /always/, on scalars, vectors, matrices,…

hi, would you mind linking to the book? https://www.jsoftware.com/help/learning/23.htm is the closest i've found, but wondering if i'm missing something perhaps, Julia? tyvm

Probably this: Kenneth E. Iverson - Calculus https://www.jsoftware.com/books/pdf/calculus.pdf

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

#590

Post by pbronez »

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...

Great article… been worrying about this one quite a bit:

> If these tools demand expertise, yet the tools can actively circumvent the friction that cultivates expertise, then what is the path for one to become an expert so they can effectively use these tools?

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