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 :)