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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

#591

Post by wrsh07 »

rlt wrote: post #431
pdpi wrote: post #374

Earlier quoted context omitted.

"OpenAI's internal team solves famous maths problem" is technically impressive but dispiriting. Non-experts solving a problem by just throwing resources at it is kind of the worst possible optics for knowledge workers. It's just disempowering. "Famous mathematician uses ChatGPT to solve famous math problem" is equally technically impressive, but now you're telling those very same knowledge workers "that famous mathem…

Then they should give grants of tokens to famous mathematicians. EDIT: oh, they do offer grants of $1000 of API credits to researchers https://help.openai.com/en/articles/10139500-researcher-acce...

Note, in posts like the following, the author indicates they are able to get free subscriptions from OpenAI

As an aside, there's this idea in math that when you create a new field you shouldn't solve all the easy problems - you need to entice other people to learn about the field!

I expect there's some element of that here. It's much better for OpenAI and Anthropic if their users are the ones discovering and writing up the results of the AI solving hard math. Look at the high school and college age students who have become ai power users and potentially learned how to use git to contribute ai generated solutions

(Related: I believe Terry has also gotten all of the subscriptions gifted to him)

https://xenaproject.wordpress.com/2026/07/20/human-mathemati...

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

#592

Post by JadeNB »

dekhn wrote: post #321
JadeNB wrote: post #201

Earlier quoted context omitted.

For what it's worth, it's not a problem with multiple kinds of multiplication (multiplication by a scalar can be viewed as multiplication by a specific kind of matrix), but with the idea that one can cancel in a multiplication. Since you can't cancel in matrix multiplication, you run into unexpected trouble when you try to do so, even if that's the only multiplication in sight. (In fact, you can't cancel in scalar mu…

P = NP is actually one of the worst abuses of symbology I've seen in math. """During his own Google interview, Jeff Dean was asked the implications if P=NP were true. He said "P = 0 or N = 1." Then, before the interviewer had even finished laughing, Jeff examined Google's public certificate and wrote the private key on the whiteboard."""

I'd call P = NP computer science rather than math, but perhaps it's reasonable to call it sufficiently on the theoretical side of CS that it really is math.

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

#593

Post by wrsh07 »

staticshock wrote: post #411
Xcelerate wrote: post #340

Earlier quoted context omitted.

I’m a bit surprised OpenAI isn’t finding these big results far faster than the product’s user base. With no limits on runtime, access to dev models, custom tuning, and top talent, you’d think there’d be a constantly running internal project with the goal of solving famous math problems. And who knows, perhaps there is, but it would be interesting to compare the rate of success per unit “effort” of the internal mathem…

You're surprised they didn't eat the tokens to churn on lots of open problems instead of asking others to pay for those tokens? They're in the token business. If they're eating the tokens, it's in support of a marketing effort, not in support of innovation across the frontier of all the other academic disciplines. The collective frontier is way too big for them to just "solve it" without asking society to at least he…

It's also much better to distribute the challenge of identifying problems amenable to which prompts

Could they do it? Sure, but to what end? It would make more people hate them and feel even more "take our interesting work." Pitching it as a useful tool just makes more sense on all levels

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

#594

Post by bdcravens »

theplumber wrote: post #464
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.

Indeed that’s the case but most of the programming problems are solved problems and unless you care how things are done someone with less/no knowledge can still make great use of programming to do what it needs to do. Let’s not pretend you need to be programmer to use AI for programming like mathematicians need to solve math problems. Programming (most of the time)solves real problems rather than abstract constructs.…

True, but I think it's the difference between doing it for a single $200 subscription vs spending $200 a day in tokens.

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

#595

Post by stephbook »

godelski wrote: post #427
napoleoncomplex wrote: post #21

This 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.

> What a world we live in. It's a really interesting world. You can spam GPT to get novel math results but here I am trying to scroll up to the beginning of the conversation and 5 minutes in I still don't know if I'm near the top yet. Scroll... wait for render... scroll... wait for render... repeat... We live in a world where there's so much crazy technology but few people use it to make products better or to improve…

> few people use it to improve people's lives.

Did Tao do that?

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

#596

Post by inigyou »

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 recently prompted ChatGPT about theoretical physics because I wanted some examples of AI slop. It affirmed my hypothesis that dark energy results from the nonzero VEV of the Higgs field. Wow! I'm so smart! I solved dark energy!

Any actual physicist would probably be able to tell me why that's a category error. I don't know why because I'm not one. But there are actual mathematics underlying a statement like that and I'm 99% sure the maths don't work like that.

By the way I think that's why everyone thinks of so many weird physics ideas more than other fields. It's because things are explained in words that hide math, and you can make hypotheses in words that would be obviously nonsense at the level of maths. Like your boss asking why you don't just recompile the cloud.

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

#597

Post by edot »

larsfaye wrote: post #436
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.

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...

Nicely written!

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

#598

Post by lanstin »

budsniffer952 wrote: post #536
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.

While humans are infallible and correct.

Math professors are remarkably good at answering math questions or solving ad hoc math puzzles correctly. Also at stepping back and asking, why are you trying to show this result, what do you think it has to do with the thing we are trying to prove. Much better at knowing when the student has gone off the path in some subtle way than the LLM (without a Prof Tao in the chat).

Professor Tao also put out some YouTubes of him working with an older LLM to do Lean proofs, and his intelligence matters - things where I would be stuck for hours trying to understand what was failing in the model proof were just instantly clear to him and fixed in thirty seconds.

And I am an ok coder (rather than a bad maths grad student), but the LLM will happily thrash around the edges of a problem with me with no clear convergence when I don’t have that clear insight and the problem is weirdly presented enough; I still find the trick to walk around the block and disengage and then return knowing exactly what to do (now prompting it to the right thing) to be a super power for getting what I want out of the coding system.

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

#599

Post by tejohnso »

It's astonishing to me that a technical conversation at that level can be had with a machine that is performing computations to statistically determine what tokens it should use based on numerical weights and relationships. It just doesn't seem like it should be able to come up with details and insights like this, assisting one of the most intelligent humans on the planet to work through something so detailed.

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

#600

Post by lanstin »

dnemmers wrote: post #588
mkagenius wrote: post #547

Earlier quoted context omitted.

Specific quirk of llms, also pretty much solved by existing thinking models. I think you guys are misunderstanding me, you can still talk to a llm to learn everything about physics or maths.

The problem is that you have no idea of what you're being taught is actually correct.

And for the harder maths you want something not just to explain the answer but to diagnose your conceptual error behind your questions. Asking the teacher after class or tutorial type systems work efficiently for a reason.
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