Posting the paper: https://arxiv.org/abs/2508.05105
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.
(n=4 for the paper, "cubic 4-fold")
https://en.wikipedia.org/wiki/Homological_mirror_symmetry#Ho...
Don't miss the caption from the end of the previous page, what the sum means :)
It was probably not intentional, though, and might trigger noone besides snobs like us :)
>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 :)