Now who wants to say ChatGPT 5.6 Sol is just another token predictor...?
Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
391–400 of 681 posts
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#392Not sure how to suggest edits to titles, but @dang: his first name is Terence, not Terrence.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#393Would Terrance Tao still be a renowned mathematician if he grew up with ChatGPT?
Would Kasparov still be a chess grandmaster if he grew up with Deep Blue?
(Yes. Chess champions are stronger than ever, even though none of them have been able to beat a computer for decades.)
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#394Imagine getting free tokens from OpenAI and the special flag on your account that tells it to "never nerf you" ?
To be clear, I've had some great success using these tools, they're amazing, but it's also very obvious that (despite it being a stochastic tool) they're clearly changing things behind the scenes a lot. GPT-5.6 for example should not be constantly tweaked without telling us. Make it 5.6.1 or something, and if you're over capacity, just say so rather than returning lower quality results.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#395Terrance 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.
A naive hope is: you see that the LLM is so good at coding that all you need to do is supply a "yes/no" on what you want.
Turns out that understanding the technical domain is important to getting good results, even if the LLM is more capable at producing output. -- It's still a case of "garbage in, garbage out".
I think for many newbies, they see the LLM is so good at programming and so figure they don't need to learn anything. Apparently not so.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#396Earlier quoted context omitted.
this sounds like like an open parenthesis ( without someone independently verifying it, it just dangles there ...
At Mozilla, we had a set of whiteboard tags we could set on bugs, like "[crash]" or "[compat]" or "[leave-open]". That last was used when there were multiple patches attached to the bug, and we wanted to land only some of them without automation closing the bug once they landed. (It's common to have alternate approaches or test cases also attached to the bug, so you normally don't want to wait for all of them to land…
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Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#397Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#398every time i see this name i think of Terrence Howard. it is quite confusing.
Funny that two of the greatest modern mathematicians share the same uncommon first name.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#399Earlier quoted context omitted.
> 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.
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…
How could they?
That's why the free market works, millions of agents in parallel beats any planned economy (by humans)
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#400What was most remarkable to me from this transcript, was how strong of an equal the AI agent comes across compared to the user (Tao). And Tao is one of the top mathematicians of modern times. Yes, Tao is guiding it to where he wants to go. But also, Tao is actively learning from it and relying on its explaining, analysis, and inference abilities. You can easily imagine this conversation having taken place between Tao…
> 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.