Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

Post by lern_too_spel » Wed, Jul 22, 2026, 7:47 PM UTC

WarmWash wrote: post #30

Math has some of the most insanely dense and impenetrable nomenclature. I can generally keep my head mostly above water or at least near the surface reading from most STEM fields, perhaps leaning on google/wikipedia a bit, but man, mathematics just so quickly decouples from all common tractable understanding it's insane. Sorry it's a bit of an aside, but I imagine many other otherwise "technical" folks feel the same…

Post by 8n4vidtmkvmk » Wed, Jul 22, 2026, 7:53 PM UTC

gowld wrote: post #130

ben_w wrote: post #70

Earlier quoted context omitted.

Aye. A decade or so ago I wondered if the reason maths was hard was the names being optimised for writing by hand. Everything's single letters if they can get away with it, so when mathematicians run out of Latin alphabet, they use Greek, bold, etc. Even integration's ∫ is a fancy elongated s. CS version would be e.g. integral(function=some_named_function, from=a, to=b, with_respect_to=argument_of_function), which ma…

Look up "APL" and "J".

Post by dekhn » Wed, Jul 22, 2026, 7:54 PM UTC

logicchains wrote: post #109

dekhn wrote: post #40

Earlier quoted context omitted.

I had a few moments of this in the past. For example, in my quantum class the teacher wrote "H Psi = E Psi" on the board, we all laughed, "just cancel the psi" but it turns out one was a multiplcation and the other was a matrix multiplication (operator) and so we had to learn all new nomenclature. Similarly, at some point somebody pointed out to me "the reason you're confused is that the bold on that variable means i…

>For example, in my quantum class the teacher wrote "H Psi = E Psi" on the board, we all laughed, "just cancel the psi" but it turns out one was a multiplcation and the other was a matrix multiplication (operator) and so we had to learn all new nomenclature. This is one of the great things about Lean becoming used for more and more mathematics: understanding exactly how an operator/function is defined is just an IDE…

Post by khurs » Wed, Jul 22, 2026, 7:55 PM UTC

I_am_tiberius wrote: post #140

Are shared chats solely secured by a uuid?

Post by ben_w » Wed, Jul 22, 2026, 7:57 PM UTC

superloika wrote: post #112

ben_w wrote: post #93

Earlier quoted context omitted.

If natural language was structured in a logically computable way, we'd have had interesting chatbots by the late 80s, basically as soon as a dictionary fit in local RAM, and for the same reason we got compilers. Da hole raisin y nat-lang be v. hard is dat i kan rite lik dis an it be cool 4 native engrish speekrs 2 unerstand. LLMs are of course fine with this sentence in exactly the way that Zork's engine couldn't be.

The underlying structure of language, which is grammar, is obviously logical. That the symbols used to represent this grammar can be sometimes fuzzy or ambiguous, is no problem for a machine that takes context and probability into account when translating words to the underlying grammar structure.