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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

#261

Post by WarmWash »

minraws wrote: post #240
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…

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, forcing you to get really close to the origin before you can "hop" over to that math vector. Other "knowledge" vectors, by virtue of being more bunched up, are closer together much further up, if that poor analogy at all makes sense.

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

#262

Post by epolanski »

jdw64 wrote: post #13

I wish you'd share some conversations from experienced programmers too. How do they ask questions?

Antirez spends weeks planning with multiple models till he has a clear architecture and understood the constraints before he writes a line of code.

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

#263

Post by randomImmigrant »

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…

Yes, the nomenclature in math is atrocious. It isn’t much better in physics or biology however. As a species, we suck at naming and classification, and keep starting new trends atop old ones. There is certainly need for the many abstractions of math to be as complex and well specified as they are. There’s no reason for their nomenclature to be so bad. The end result is a substantial portion of the population, which can certainly hold and manipulate abstractions, fails to even contend with pure math. I do think visualization tools will help in the future, to demystify some of this. But as with all sciences, the need for personal glory/mentor deification often conflicts with broader explainability.

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

#264

Post by Planktonne »

hyperpape wrote: post #245
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…

I studied math through college before learning to program as an adult and becoming a software engineer, and I strongly disagree. I don't know how to say this in a way that won't sound insulting, but I don't mean it to be insulting. Programming, even systems engineering, is a surprisingly shallow field. I don't mean that it's easy--it's not, it can be incredibly difficult. Difficult and deep are just different concept…

> Programming, even systems engineering, is a surprisingly shallow field.

I agree, and I don't think we should be at all ashamed of this.

The beauty of programming is that we can produce incredibly complex and powerful things by manipulating a small set of simple constructs together. There are only a few core tools--iteration, conditionals, etc.--but they can be snapped together into much more capable configurations.

Good programming is the art of deconstructing complex behaviour into these few constructs, and that's really fascinating.

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

#265

Post by colordrops »

OJFord wrote: post #56
colordrops wrote: post #51

Earlier quoted context omitted.

I'm not sure an AI will speed things up much. You would probably still need years of layers of foundational understanding to get the advanced material. We don't go through years of school to learn math just because teachers are bad - it's because complex subtle ideas are built on countless other ideas, and aren't necessarily compressible to something every layman can understand.

The years are broad though, the nice thing with AI explanations is that they can go deep quickly, and quite precisely down the path you need for your prior experience.

Oh for sure, I'm not denying the value of AI as a teacher, just saying that it's not going to speed things up much over a quality personal teacher/tutor.

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

#266

Post by auntienomen »

minraws wrote: post #151
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…

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…

Yeah. In math at least it's clear that you don't know what's going on. In other fields, it's very easy to think you understand without knowing how much you're missing.

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

#268

Post by HPsquared »

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…

Mathematics has a lot of knowledge points that do connect to the "real world" very deeply, but perhaps the nature of their linkage to other mathematical pieces of knowledge is best left to the mathematicians. But we can still use the pearls of wisdom that come out of the process.

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

#269

Post by customguy »

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…

Is there something that translates math formula into code? There are many (comparatively) "simple" algorithms I simply cannot make heads or tails when they are described via math prose or math formula, but when it's code I basically instantly know how to rewrite it into any other language I know, at least, and sometimes that's a starting point for poking at it to understand it a bit better, if not the same way would if you understood all the underlying math.

For poor old me, too many wikipedia articles on algorithms useful mostly or only for programming are described in formulas rather than simply code with detailed comments. Scrap the whole page and just gimme the code :( Not even to copy and paste, because that's a language I can understand, and enjoy learning.

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

#270

Post by WarmWash »

mrpf1ster wrote: post #236
umvi wrote: post #227

Earlier quoted context omitted.

No, the problem with mathematics is that it is basically its own language separate from your native tongue. You have to learn dozens of symbols and greek letters and such and memorize what their meaning is in the context of mathematics in order to "follow" a mathematical conversation. Mathematics would be much more approachable if it just used plain English like `sum(0, Infinity, my_func)` instead of a big Greek sigm…

Your translation only makes intuitive sense to you because you are well versed in programming. I suspect if I showed a non-technical person with no background in either math or programming they would think both are nonsense until you explained it to them

The thing is that you basically cannot explain the math like you can the programming.

Tables, algos, and variables are all things people can generally quickly grasp. The construction is abstract but the function is tangible.

The math is working entirely on abstract objects, using abstract tools, governed by abstract rules. It's just all so desperately far away from anything even technical people have contact with.

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