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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

#452

Post by stkdump »

eh_why_not wrote: post #254
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…

Agreed, it's stronger "horizontally". But I also think that we're not far away from it being stronger vertically; i.e. superior to Tao, in that such turn-by-turn guidance by him in solving sophisticated and difficult problems will not be necessary for long.

I strongly suspect that the horizontal and the vertical strength are not perpendicular. I suspect having a very wide knowledge gives you access to patterns that reproduce across fields that an expert would lack.

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

#453

Post by nxobject »

estetlinus wrote: post #432
godelski wrote: post #427

Earlier quoted context omitted.

> 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…

Better than a 2026 human, worse than a 2016 machine. You win some, you lose some, I guess...

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

#454

Post by eru »

SOLAR_FIELDS wrote: post #388
appplication wrote: post #313

Earlier quoted context omitted.

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.

Maybe! But I suspect you can write a little LLM assisted helper to at least make your prompts sound more like Tao's. (Your ideas won't necessarily be better, but you can probably 'imply a weighting towards an extremely abstract and high level rigorous corpus'.)

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

#457

Post by lattalayta »

minimaxir wrote: post #106
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 For posterity, this indeed works for most problems where an agent might give up. LLMs don't inherently know something is impossible. The phrase I tend to use in my harder prompts to automate this with a sane loop breaker: > **REPEAT THIS PROCESS UNTIL CONVERGENCE AND YOU ARE OUT OF OPTIMIZATION IDEAS.** You have permission to keep iterating.

Maybe it's just me, but does anyone else feel goofy speaking to a computer this way?

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

#459

Post by eru »

timacles wrote: post #406
retrochameleon wrote: post #300

Earlier quoted context omitted.

Hopefully in decades hallucinations will be largely solved.

its just as likely hallucinations will only get worse because their source data will be riddled with hallucinations

You can't hallucinate a working lean proof.

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

#460

Post by divyekapoor »

CamperBob2 wrote: post #362
skeledrew wrote: post #39

Earlier quoted context omitted.

I encountered something fairly similar working with Claude a few days ago. For a current project I've been fairly hand-wavy with requirements since I was getting good results, but it seemed to be failing hard on some key points, so I started to be more strict with it. Even after the fails were resolved, I've noticed that Claude now behaves differently within that project, carefully checking and rechecking things up f…

The most powerful way to use Fable in particular seems to be to pit it against Sol as a reviewer (or, I suppose, vice versa.) After going back and forth a half-dozen times, the result tends to be pretty much bulletproof. What's somewhat disturbing is just how much Fable's code really does benefit from the review. It tends to leave a lot of low-hanging fruit, and you can see it getting kind of impatient when repeatedl…

What are you using to put Fable and Sol on each other?
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