Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

Post by efebarlas » Thu, Jul 23, 2026, 6:08 AM UTC

School-Cotton wrote: post #219

the8472 wrote: post #178

Earlier quoted context omitted.

Yeah that's pretty much what gwern argues here[0]. Or to adapt another proverb: to predict the next token you first need to model the universe. [0] https://gwern.net/scaling-hypothesis#gwern-difference--effic...

> to predict the next token you first need to model the universe Exactly. The "most likely next" series of tokens, for example, when given the first half of a correct mathematical proof, is the correct rest of the proof. I have never seen anyone define "most likely next token" in such a way that this isn't true.

Post by pertymcpert » Thu, Jul 23, 2026, 6:20 AM UTC

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...

Post by mkagenius » Thu, Jul 23, 2026, 6:25 AM UTC

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.

Post by mettamage » Thu, Jul 23, 2026, 6:34 AM UTC

ProllyInfamous wrote: post #463

Frost1x wrote: post #338

Earlier quoted context omitted.

I had a similar reaction with the language but also response times and language. It reminded me of a quote about Jon von Neumann from Edward Teller: "Von Neumann would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us."

Von Neumann is an interesting historical character that nobody has ever heard of , e.g: for such an accomplished inventor, that so few minutes of video footage exist of him. >I sometimes wondered if he used the same principle when he talked to the rest of us. I can come pretty close to a humbler example of this, as the more-extroverted "bad twin," of an identical set: my own genetic equal is bored to tears interactin…

Post by mettamage » Thu, Jul 23, 2026, 6:37 AM UTC

larsfaye wrote: post #438

noosphr wrote: post #400

Earlier quoted context omitted.

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 hum…