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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

#431

Post by rlt »

pdpi wrote: post #374
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…

"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...

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

#432

Post by estetlinus »

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…

And I am still waiting for the Apple Reminders AI to sort Milk in the right category…

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

#433

Post by [deleted] »

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.

[deleted]

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

#434

Post by qsera »

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.

> just repeatedly saying "keep going" to ChatGPT

>What a world we live in.

Not sure, it sounds pretty boring to me...

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

#435

Post by meowface »

kittoes wrote: post #410
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.

https://x.com/Kittoes0124/status/2079386024753443324 I'll have a third for you soon, here's the obligatory result in a tweet. A detailed post about it is in the works.

It's going to be pretty crazy when GPT-6 comes out, since the rumors are it's quite a bit smarter and wiser than GPT-5.6.

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

#436

Post by larsfaye »

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.

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...

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

#437

Post by kittoes »

meowface wrote: post #435
kittoes wrote: post #410

Earlier quoted context omitted.

https://x.com/Kittoes0124/status/2079386024753443324 I'll have a third for you soon, here's the obligatory result in a tweet. A detailed post about it is in the works.

It's going to be pretty crazy when GPT-6 comes out, since the rumors are it's quite a bit smarter and wiser than GPT-5.6.

Maybe, but I want to point out that even the lesser models are capable of hunting this stuff down. The most important thing is that you provide a decent path for them to follow.

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

#438

Post by larsfaye »

noosphr wrote: post #400
john_strinlai wrote: post #248

Earlier quoted context omitted.

> Maybe a year - or two model releases - from now, the AI assistant will be undeniably stronger than Tao, and not an equal anymore. we're kind of well past that (in my opinion), if you consider that this is the same ai assistant that can help you with a recipe, diagnose a weird sound in your car, help with biology homework, translate languages, and so on. even in math alone, i think its indisputably already stronger…

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 humanity, and extract data via an algorithm that is highly adept at sorting through it.

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

#439

Post by saimiam »

slidehero wrote: post #429
nozzlegear wrote: post #426

Earlier quoted context omitted.

> that's some Harry Potter kind of "writes itself" book. I'm sure people thought calculators and, indeed, computers themselves were very Harry Potter as well when they first came out. But in the fullness of time the magic and mystique has drained away, and we're left with the understanding that they're just tools. > at this point, for me, any comment about LLMs that begins with "it's just ..." is hard to take serious…

>I'm sure people thought calculators and, indeed, computers themselves were very Harry Potter nobody thought that

In my circle, some people certainly thought computers were basically magic.

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

#440

Post by Geof25 »

bredren wrote: post #209
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…

It is ~a meme on subreddits that developers struggling to get good results out of any given model is a "skills issue." But I think your comment drives at some authentic take on this. Skill with AI is not only crafting iterative prompts the agent will understand, but also very high domain-specific knowledge of what the prompts explore. One without the other can result in frustration or worse.

It is a skill issue. Such developers have to take a problem, isolate it and explain it to someone/something else with enough context to be able to work with it.

It is perplexing how many developers lack this basic skill, some of them borderline lack theory of mind and are incapable to understand that other people can't see the unspoken part in their heads.

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