Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

Post by AgentME » Thu, Jul 23, 2026, 2:00 AM UTC

superloika wrote: post #55

IshKebab wrote: post #14

Earlier quoted context omitted.

> there’s no “intelligence” there BUT There is clearly intelligence there. We have no way to recognise intelligence other than the appearance of intelligence and this very clearly displays that. It's also quite clearly different to human intelligence in some notable ways, but not in any that preclude describing it as intelligent. At least for normal non-pedantic definitions of the word.

There is no intelligence. If anything, this just shows that natural language and mathematics are both fields which are structured in a logically computable way. And if you have a machine that can compute symbolic logic, you can process both natural language and mathematics. A second corollary is that rational consciousness and thought is less likely to be contained in language than previously thought, because if lang…

Post by ValentineC » Thu, Jul 23, 2026, 2:02 AM UTC

epolanski wrote: post #252

ValentineC wrote: post #202

Earlier quoted context omitted.

One thing I've repeatedly told people is that chatbots are often the most patient teachers we'll ever get (especially when explaining "stupid" questions) — compared to what we've encountered on StackOverflow or Reddit.

They lack the empathy to understand where and why you're struggling. I've given private math lessons and seen students struggle with ai, even though ai gave the right answers. My intuition is that humans spot xy problems easier when teaching (user ask x but really needs y), whereas llms will oblige writing about x.

Post by gaigalas » Thu, Jul 23, 2026, 2:08 AM UTC

Xcelerate wrote: post #340

minimaxir wrote: post #106

Earlier 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…

Post by floam » Thu, Jul 23, 2026, 2:19 AM UTC

rubyn00bie wrote: post #379

minimaxir wrote: post #106

Earlier 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’ll have to try this exact phrasing. I had a lot of trouble with GPT 5.5 more or less completely ignoring similar prompts and instructions and entering a sort of “doom loop” or just consistently trying to prematurely end the chat. I would love any tips for other folks who have successfully used similar approaches.

Post by versteegen » Thu, Jul 23, 2026, 2:24 AM UTC

aleph_minus_one wrote: post #336

ChrisClark wrote: post #303

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But... what is a ring? What is a formal variable? What is a vector space? What does "algebra over the ring" mean? His point is the terms are dense too

> But... what is a ring? What is a formal variable? What is a vector space? What does "algebra over the ring" mean? All these terms were taught to computer science (and of course math, physics, ...) students as part of getting their degree in computer science, because these concepts are important for many algorithms.