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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

#291

Post by jakeinspace »

Jtarii wrote: post #221
minraws wrote: post #206

Earlier quoted context omitted.

Again, you are underestimating how much effort it takes to understand how an 8086 CPU works. There are a lot of foundational concepts that you are simply assuming the person already understands. That may be a reasonable assumption for a CS undergraduate, but the average person does not understand binary arithmetic, registers, memory addressing, instruction execution, calling conventions, or even what a CPU is doing a…

> There is an enormous amount of computer science that most programmers are completely unfamiliar with, especially within academic CS: programming-language theory, type theory, formal semantics, compiler theory, algorithmic research, complexity theory, distributed computing theory, verification, cryptography, computational geometry, numerical methods, and so on. Being proficient in one narrow area does not automatica…

Every quantifiable science has some amount of math, but it's by definition applied math. I think this was more of a debate between applied and more abstract math.

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

#292

Post by jameshart »

WarmWash wrote: post #224
minraws wrote: post #151

Earlier quoted context omitted.

This is also true for almost every other field, even within computer science. The only difference is that a lot of people operate at a very surface level without realizing just how much background knowledge they have accumulated. Think about the number of keywords your average SWE is expected to know. It is rather insane. Cache, stack, heap, process, thread, socket, file, tcp, http, tls, websocks, socks, soc2???, dea…

> 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…

> 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.

Careful, I think you might be committing an https://xkcd.com/2501/ error.

What even is a protocol? What is a host? What is a ‘stream of octets’? Wiki helpfully tells you octets are also known as ‘bytes’.

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

#293

Post by minraws »

WarmWash wrote: post #261
minraws wrote: post #240

Earlier quoted context omitted.

You are comparing TCP a relatively basic topic in the grand scheme of computing with Rees_algebra which is fairly specialized, we could take a simpler topic more foundational and clearer to understand and compare them. I can understand that this feels like one is so much more complicated part of it is also how the articles were written, wikipedia is not known for quality maths explanations. But beyond that this compa…

I think you are snagging on thinking this is an observation about difficulty, time-to-mastery, or mental firepower requirements. It's not. It's a plain observation that math exists on mostly it's own path with little to zero overlap with our lived experiences. If mathematics was a vector, it would have similar magnitude to other vectors, but it's direction would be much more removed from the typical knowledge pack, f…

Very true, I feel like the sense that Computing is easy comes from the inherent closeness of our lives experiences to it. Everyone uses a Phone they see ram understand memory, can understand process and processing.

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

#294

Post by neelm »

WarmWash wrote: post #30

Math has some of the most insanely dense and impenetrable nomenclature. I can generally keep my head mostly above water or at least near the surface reading from most STEM fields, perhaps leaning on google/wikipedia a bit, but man, mathematics just so quickly decouples from all common tractable understanding it's insane. Sorry it's a bit of an aside, but I imagine many other otherwise "technical" folks feel the same…

I agree. I think the distance in capabilities between great mathematicians can be so much more vast than other fields as well. Some of them need every step to be derived, while others can skip ten in their head.

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

#295

Post by mohamedkoubaa »

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?

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

#296

Post by lucassz »

jameshart wrote: post #292
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…

> 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. Careful, I think you might be committing an https://xkcd.com/2501/ error. What even is a protocol? What is a host? What is a ‘stream of octets’? Wiki helpfully tells you octets are also known as ‘bytes’.

I agree with you here, but what's special about tech is that many of us learned all these terms fully casually while using computers as children and teenagers, which would be much less common for a chemist. That makes programmers see a lot of things as computer literacy that most people have rather than specialized knowledge.

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

#297

Post by avisser »

jameshart wrote: post #292
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…

> 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. Careful, I think you might be committing an https://xkcd.com/2501/ error. What even is a protocol? What is a host? What is a ‘stream of octets’? Wiki helpfully tells you octets are also known as ‘bytes’.

My argument is that all the vocabulary for computer science are things. Even if they are virtual, they are tangible. You can draw a picture and label a box "bytes".

Nothing in the ChatGPT conversation is tangible. It's all in the realm of concepts.

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

#299

Post by chongli »

sebmellen wrote: post #220
ndriscoll wrote: post #186

Earlier quoted context omitted.

Nope, math notations are optimized for reading, not writing (consider that people still use symbols on computers despite it being quite a bit more tedious to type). The conciseness makes it easier for you to see structural patterns and do symbolic manipulation in your mind's eye. Even something basic like the wave equation would become completely illegible with an expanded notation like that. Same reason why we write…

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 objects, and then join those to yet another set of objects and the results of their operations, ad infinitum, ad infinitum..."

People genuinely struggle to think verbally or visually once we extend beyond 3 dimensions and start talking about infinite-dimensional constructs, uncountable sets, and so on...

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

#300

Post by retrochameleon »

singularity2001 wrote: post #249
vouaobrasil wrote: post #166

Earlier quoted context omitted.

> 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 what will happen though to future generations: they won't be able to use it for anything because none of them will have the "decades of coding" experience that you have had the privelege to have without AI.

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.
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