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Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
381–390 of 681 posts
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#382"Continue the search. Have a clear strategy obtained from deeper understanding of the problem structure."
And a new system prompt stanza was fledged.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#383This is the second ChatGPT shared conversation I've seen today that is truly fascinating. The first one was someone proving another conjecture false by just repeatedly saying "keep going" to ChatGPT: https://x.com/DmitryRybin1/status/2079904005652893709 What a world we live in.
I've noticed GPT specifically has more of a tendency to stop partway through things than many other models do. Although my most recent experience with it was 4.X I believe. Hearing "here's what I've done, here's the completely unambiguous next steps, I'll wait for you to send a pointless message before I continue" over and over again is a real pain.
That was a tendency of 5.4 and earlier, OpenAI specifically worked to avoid it in 5.5 and I find it happens rarely know. It really felt like 5.4 had been intentionally trained to stop and check, I believe it wasn't the system prompt.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#384This is the second ChatGPT shared conversation I've seen today that is truly fascinating. The first one was someone proving another conjecture false by just repeatedly saying "keep going" to ChatGPT: https://x.com/DmitryRybin1/status/2079904005652893709 What a world we live in.
>> This is the second ChatGPT shared conversation I've seen today that is truly fascinating.
We recently had some bugs fixed in the geometry kernel of solvespace. Not much conversation, but the analysis from the AI was amazing:
https://github.com/solvespace/solvespace/pull/1729
https://github.com/solvespace/solvespace/pull/1730
https://github.com/solvespace/solvespace/pull/1731
From the Validation section of PR 1730:
"The model family was reconstructed programmatically (parameterized cuboid stack) and swept over 2,304 configurations — extrusion directions, workplane-normal orientations, sketch windings, D's plane/height/depth/extent, including all the exact-coincidence heights. Zero failures with the fix; 576 failing configurations without it. The generator is available on request."
It looks like it wrote a python script to generate test cases in our file format for testing. Just... you know, as a side quest.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#385It’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.
> I can't use it for theoretical physics because I can't evaluate the responses.
A tool, even if it is a chisel, in the hands of a master sculptor would obviously result in a wildly different outcome.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#386It’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…
Yes, the AI models are so useful in areas where you are an expert and can guide it in a useful way. I use multiple chats delay to help figure out client projects.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#387Earlier quoted context omitted.
My example was contrived, I'm sure some smart people could come up with a SQL-esque language that is even more readable to non-technical folks than programming syntax. At a certain point though, your layman has to know the "atomic" (as in, you can't break them down further) mathematical concepts like "functions" and "infinity": `sum function(x) from x=0 to x=infinity`
I'm sure some smart people could come up with a SQL-esque language that is even more readable to non-technical folks than programming syntax. And somehow, none of the thousands of very smart mathematicians have done that, or if they had, it has not seen wide adoption. I recommend contemplating on this: if math could be made easier by changing notation, why hasn't this already happened?
Momentum, mainly. Richard Feynman invented a more intuitive triangle-based syntax for sin/cos/tan/etc but eventually abandoned it and conformed with mathematical norms for the sake of ubiquity.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#388Earlier quoted context omitted.
There may be something(s) about mathematics (proofs) that makes it particularly amenable to LLM reasoning - highly inductive from facts that are explicitly within-context/associative space? Being an unusually well documented discipline in general, with less influence from tacit knowledge or idiosyncratic “it works however the opinionated human made it work +- bugs” processes? Something about simulating even the small…
There’s also probably a lot less noise from casual internet conversations. I imagine a nontrivial amount of what LLMs know about certain technologies comes directly from forums like reddit where quality of response isn’t guaranteed.
I mean, just the way Tao phrases these inqueries seems to imply a weighting towards an extremely abstract and high level rigorous corpus. In a way, prompt engineering really is the big unlock here.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#389Earlier quoted context omitted.
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.
A ‘Byte’ is not a concrete thing and the fact you think it is speaks to the degree to which you have immersed yourself in a mental model which thinks of ‘information’ as if it is a real concrete thing, to the extent that you don’t even realize the levels of conceptual abstraction you needed to build in order to internalize what a ‘byte’ is.
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.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#390This 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!
Oh, GPT-3.5, recognizable in so many old screenshots by the green icon. If ever a popular model deserved the term "stochastic parrot", it was GPT-3.5. I wonder what percentage of people today still base their opinions of AI capabilities on their experiences with that model. That model was the only option for free ChatGPT users for the first year and a half of ChatGPT's existence, from November 2022 to May 2024.