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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

#131

Post by tcp_handshaker »

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…

That is one of the things that fascinates me most about mathematics compared with other fields, and it led me to discuss the subject with professional mathematicians. The funny thing is that they admitted it is the same for them...stray even slightly outside their own specialized area, and within two or three lemmas, they also feel completely lost.

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

#132

Post by WarmWash »

vector_spaces wrote: post #89
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…

Yeah it is a lot of simple ideas stacked one on top of the other, but the edifice is so large from some vantages that the building blocks aren't visible, or tractable to think about independently. And sometimes the ideas are very subtle, so you can only develop fluency partly by spending lots of time playing with those blocks by building your own little structures. You also develop fluency by talking to other mathema…

Yeah this is pretty much where I am at. Take the phrase from one of the responses

"The special fiber is the associated graded ring.....and that the filtration admits sufficiently simple homogeneous lifts of the three generators, then one might prove"

In any other context I would at least have some degree of intuition about what is being discussed, but in in math? Absolutely no idea. And usually if I start digging and turning over stones to uncover meaning, I'm just met with even more totally dense code-word language. Unlike other fields were digging is usually quick to relieve ignorance, somehow in math it tends to get worse.

I'm sure I am capable of grasping this if I took the time, and perhaps even what is being discussed it rather intuitive, but the incredibly density of the nomenclatic swamp you have to trudge through for math is totally unrivaled.

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

#133

Post by gowld »

taylorfinley wrote: post #114
axus wrote: post #9

"I’ve activated Pro. Can you continue to look for a potential geometric explanation of the X_3 ~ A3 miracle that avoids coordinates or other unmotivated constructions ?" Another satisfied customer!

Came here to flag the same beat. It's wild to me Terrance Tao has to pay to talk to chatgpt, you would think it would be the other way around!

"Activating Pro" doesn't mean "paying". It means selecting a slower/smarter model.

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

#134

Post by Diogenesian »

anthonypasq wrote: post #110
Diogenesian wrote: post #45

Earlier quoted context omitted.

[flagged]

> If AI researchers cared about scientific thinking, they would be intensely focused on the brains of bees. Basically every academic AI researcher in history was doing what you described. The AI industrialists stopped caring 6 years ago once they realized LLMs seem to have been the only thing in 80 years that actually seems to work at any useful level. There are plenty of pioneering scientists who are either returnin…

> Basically every academic AI researcher in history was doing what you described.

That is not true. Alan Turing did not view things that way, his test would say that a dog has zero intelligence. Neither did any of the MIT Lispers. And neither do Lecun or Sutskever or Sutton! They are all focused on human intelligence. None of them are even slightly concerned about an AI which is intelligent before it learns any language.

> the only thing in 80 years that actually seems to work at any useful level

This isn't true either! Mathematica / Maple / etc are "old-fashioned AI" and they obviously work. The Lisp expert systems were also useful, though less so than an LLM.

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

#135

Post by LeifCarrotson »

kypro wrote: post #66
personalityson wrote: post #60

This was my conversation with ChatGPT 4 years ago: https://i.imgur.com/WPaWgzZ.png Where will we be in another 4 years? What a time to be alive!

I'm from the UK. What's in the image?

You can't view a random imgur screenshot in the UK?

What image hosts work for you? Imgbb? Postimages?

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

#136

Post by petesergeant »

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…

I think we have a couple of years of "being good at talking to the LLM about your field of expertise" being a useful human skill, until that too gets washed away

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

#137

Post by purple-leafy »

I’ve had a similar experience using LLMs to have mini personal breakthroughs.

One thing I notice is many models say statements along the lines of “okay we have exhausted this thread it’s diminishing returns from here and we should stop and move on”

It’s funny because I’ve been building a tiny neural network maze solver (23 bytes solves 92.75% of unseen 2D mazes)

When I asked ChatGPT/Fable if we had anymore threads to pull to increase capability and decrease byte size, they both basically said no way - back when I was at ~166 byte models with a ~85% solve rate.

Throughout the experiment I just kept trying different approaches and eventually had 3 mini “breakthroughs” in this particular niche. But if I had listened to the models…

Anyway, these models are amazing to experiment with quickly, but they are dumb as hell and so absolute

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

#138

Post by breezybottom »

overfeed wrote: post #120
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…

Math strives to minimize ambiguity, which other fields don't do as much. Non-math fields tend to reuse regular words as jargon (i.e. with specificity of meaning that may fly over the laymen's heads). Social sciences and humanities are most notorious for this, often resulting in non-practitioners not realizing they are out of their depth because they are not looking at symbols from non-Roman alphabets.

That's something only someone who's never studied advanced math could say. Math notation and jargon can be extremely ambiguous and overloaded. "Normal" has about 20 different meanings.

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

#139

Post by breezybottom »

globular-toast wrote: post #97
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…

It's just language. Mathematicians don't invent notation for fun, they do it because they naturally start thinking at a higher level of abstraction. If you're not thinking at that level then, well, it will be all Greek to you.

Sometimes they do. There's nothing divine or necessarily rational about notational standards, which can vary greatly even within the same field.
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