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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

#621

Post by lanstin »

Myrmornis wrote: post #579
dash2 wrote: post #521

Earlier quoted context omitted.

Yeah, as a scientist I can read most Science or Nature articles in most fields, and get a rough idea. Not every piece of jargon, but I can understand roughly what they did, read the graphs and figure out the result. A friend sent me his maths PhD and I did not understand a single sentence .

That's not because the nomenclature is bad, it's because the concepts in advanced mathematics are further from our familiarity zone. In other words because it's hard.

Both unfamiliar and hard. :)

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

#622

Post by dsego »

case wrote: post #486
mkagenius wrote: post #485

Earlier quoted context omitted.

> I can't use it for theoretical physics because I can't evaluate the responses. I think pretty much the opposite. I can ask it to explain to me in ways I understand it. Even drill down the simplest of equations. Since llms have infinite patience. All I need to learn anything is patience.

I think the issue is that LLMs can be so confidently and convincingly wrong about anything. And if we (LLM tool operators) don’t know the subject matter in question, we can’t easily distinguish what they are right or wrong about.

It's not just what they output, it's also what they omit. I've unfortunately seen this when doing research on medical issues, and it gives you a false sense of having an understanding. It never warned me to watch out for symptoms that weren't specifically discussed in the context, or that some symptoms could be a different underlying condition.

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

#623

Post by literalAardvark »

dnemmers wrote: post #575
satvikpendem wrote: post #503

Earlier quoted context omitted.

The paradox is analogous to AI poisoning its own training data as more and more AI generated content is released on the Internet. Indeed, I see a hard terminus for both man and machine at some point.

Absolutely right. First gen models are trained on 'virgin' non-LLM output. Subsequent models are tainted by ingesting AI replies. Rinse and repeat, and all you end up with is AI copies of AI replies, and the noise will completely overtake the signal.

I'd have been more worried about that had the models not gotten incredibly good over time.

But they did get good and this seems like a non-issue.

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

#624

Post by XCSme »

michaelchisari wrote: post #12
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…

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 agree. I (15+ years of coding) feel like I'm 100x more productive now using LLMs to code.

But I don't think a beginner would have the same experience. The AI still makes A LOT of stupid mistakes and decisions, but I catch them early enough (sometimes while it's still showing it's reasoning steps), stop the prompt, guide it on the right path, rinse and repeat.

Sometimes I am lazy and give the AI a broader prompt, let it do its thing, and then I come back to see that it spent 90% of the time working on some part/feature/implementation that was not really needed and that it over-engineered the solution.

I rarely write any line of code know or manually change any code, I tell the AI how to do it and what to watch out for. Many times it catches some edge-cases before I even haven to think about them. I do still feel like both me and the AI could miss some edge-cases now, because I'm thinking less about the implementation and what problems can arise, but I feel like 90% of "gotchas" are already engrained in my planning after so many years of coding and problem solving.

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

#625

Post by cootsnuck »

larsfaye wrote: post #438
noosphr wrote: post #400

Earlier quoted context omitted.

It only has that depth because you prompt it towards the experts that understand that depth. An example that happened 10 minutes ago: contracts in racket, it kept arguing that you can't use -> in a contract of a function with a rest argument. I had to mention ... explicitly that it wrote the code correctly.

Yeah...I know I should be massively impressed, and I am to a degree, but isn't this what we should expect? LLMs can pick up on patterns that no human can see. In that sense, they really are a type of "search engine", but I use that term loosely. Tao is using them as a way to sift and sort theories and information that the model has a plethora of training data on. It's like being able to converse with the codex of hum…

Also I feel like people are not noticing in Tao's chat that chatGPT fairly often is doing web searches. So it literally is acting as search engine sometimes, and that too is incredibly effective when done right. So in addition to Tao using his prompts to "search/sift through vector space" the LLM is also literally just searching the web to augment its "knowledge" at inference time too.

Which, to me, again demystifies these tools. They are incredible tools, but still "just" such.

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

#626

Post by seanhunter »

mkagenius wrote: post #491
case wrote: post #486

Earlier quoted context omitted.

I think the issue is that LLMs can be so confidently and convincingly wrong about anything. And if we (LLM tool operators) don’t know the subject matter in question, we can’t easily distinguish what they are right or wrong about.

They are solving jacobian conjectures, I don't think they will hallucinate till masters level of any subject. Edit: do give counter examples if you have any in maths, physics, chemistry, biology etc

Here you go https://claude.ai/share/c8407777-1ccf-402b-9010-7bc57228b943

I asked Opus 4.8 to critique my algebra notes (these are definitely not masters level- just undergrad second year). It hallucinated an error it claimed I made in the notes and then put in a correction I didn't need because what I had written was correct.

What I said in my notes was:

   Notice that a cyclic group is a degenerate (in the sense of "smallest
   non-trivial") case of a finitely generated group where the generating set is
   a singleton.
It left-off the "non-trivial" and said that what I said was this was the smallest case of a finitely-generated group which is incorrect because it excludes the trivial group.

The point is I see the LLMs as a "smart friend"/colleague I can work with but I do think critically about what I get told and don't just take it as face value because it's not always correct for sure even in relatively basic cases like this.

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

#627

Post by smsm42 »

Kon5ole wrote: post #550
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...

Good writeup, and certainly food for thought. I wonder if this key point actually holds though: >The skills to do so, however, are a function of someone who has experienced the friction and challenges over time that culminate in "good taste". It's certainly sometimes true, but I don't think it's a general rule. Sometimes friction is just friction and sometimes you spend 1000 hours learning something that disappears a…

> Everything you know about 6800 assembly will not make your note-taking app any better.

It could. It could make a simple note-taking app not take gigabytes of memory and take visible delay on each click. Most people don't bother of course because simple note-taking app is not worth the effort. It's possible to do better, it's just often not practical.

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

#628

Post by tensegrist »

jvanderbot wrote: post #574
mohamedkoubaa wrote: post #295

Earlier quoted context omitted.

Hold on isn't this how math professors used grad students for hundreds of years?

"used" is a bit loaded, but this is just how people talk to eachother when they are thinking really hard about something they want to solve. So, I'm fairly sure it goes back as far as speech. It's just debugging - "What if it was caused by xyz", "What if we tried abc"

yeah it's pairing by another name

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

#629

Post by mrguyorama »

amelius wrote: post #532
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.

But the AI can teach you to do theoretical physics, by guiding you through materials it selected for you, helping you with questions, etc.

Being good at "generating text" doesn't make you a good teacher. It was trained on internet users, not trained educators.

Most people posting on the internet, especially people who know about more complex subjects, are terrible teachers. Teaching is it's own skill

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

#630

Post by macintux »

lanstin wrote: post #614
jbenjoseph wrote: post #506

Earlier quoted context omitted.

Even the standard RSI prompt will be like (or probably already is): "Improve yourself, make some breakthroughs, think really hard and don't give up until you are improved and make no mistakes." Eventually there will be an AI that will be able solve those sorts of questions as simply stated, like "cure all human diseases. also, make no mistakes!".

That would only be physically possible if all the data about biology was accessible. Given we routinely find new biological facts that contradict prior beliefs about how cells work, it seems likely that this day of total biological information access by humans and our creations is some time off. Reasoning ability is a limit sometimes, but we have had reason for a long long time - a solid persistent corpus of good dat…

That bothered me decades ago, when I heard people suggesting we no longer needed animal trials, we could just simulate human biology for testing.

Don't get me wrong, the way we collectively treat animals is evil, but the idea that somehow we know enough about biology even today to reliably simulate drug behaviors seems unlikely.

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