EDITED to emphasize that the idea Kontsevich "took from string theorists" is not as big a deal as title of TFA implies, thanks sno129
On page6 is the crucial^W main idea that Kontsevich took from string theory, the Hodge Diamond
It's memorable, at least :)
En.wiki has a quick explanation
Mirror symmetry translates the dimension number of the (p, q)-th differential form h^(p,q) for the original manifold into h^(n-p,q) of that for the counter pair manifold.
I wouldn't consider the Hodge diamond the "crucial idea from string theory." It's a pretty basic/fundamental concept in geometry and really doesn't a priori have much to do with string theory. The decomposition they give on page 6 probably predates most of the development of string theory.
I "blame" Quantamagazine for this.. upselling string theory via Kontsevich, because I don't think there's anything in this work related to string theory other than the Hodge diamond + related "elementary" symmetries (see my other unedited comment in response to a geometer)
It was probably not intentional, though, and might trigger noone besides snobs like us :)
There's different ways to define "related", here what does Quanta explicitly claim is "related", plausibly without looking maybe they meant historically related but not conceptually related.
Tbf I was maybe a bit indignant over this sentence from TFA:
>The proof _relies_ on ideas imported from the world of string theory. Its techniques are wholly unfamiliar to the mathematicians who have dedicated their careers to classifying polynomials.
They should have said "differential geometry", unless you count Kontsevich himself as a string theorist (maybe he does. I don't know)
From the paper, sec3.1.2:
While historically prevalent in the mirror symmetry and Gromov-Witten literature, the complex
analytic or formal analogues of an F-bundle will not be useful for constructing birational invariants
directly
Later on, however:
One largely unexplored aspect of Gromov-Witten theory is its algebraic flexibility..
I guess we can't really not credit the string theorists if Kontsevich can be so inspired by them :)
I am slowly coming around to the same conclusion. It isn't always clear how some agent types are different from others. Sometimes the prompts expect JSON blobs and sometimes they expect something else. I tried it out because I could see the potential, but I dont think it's architect-ed in a way that is suitable for things beyond simple PoCs.
It would probably be much better to start with the basic OpenAI API and then build on top of it.
What I find particularly frustrating is the difficulty in easily interfacing with my existing python tools (not like add two numbers, but somewhat complex analytics on top of structured data). If anybody has any success with interfacing with existing tools/scripts, would love to know how people are going about doing it.
Once again these are not courses per se, but do provide intuitive explanations for how transformers work. There is also the nanoGPT series of videos by Karpathy on youtube. First video here: https://www.youtube.com/watch?v=kCc8FmEb1nY
