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 :)
My academic work was very close to June Huh's; my Ph.D. thesis was directly inspired by his Fields Medal winning work. His accomplishments have undoubtedly moved the field forward and connected various ostensibly disparate areas of math, not to mention he is one of the clearest writers and speakers in all of mathematics.
There are very few people in pure math that care about transformers; they have had practically zero impact on the sort of research mathematics that the Fields Medal is concerned with.
I'm assuming you don't have a Ph.D. if it sounds generic to you. I think it's really impossible to explain to somebody who hasn't gone through it how much a Ph.D. changes the way you think.
Whether it's worth the time investment is another matter, however, which I'll leave alone.
I have not been paid because my salary is funded by an NSF grant and they've shut down the payment system and cancelled payments. (It is still down.) I'm not in the social sciences, I'm in mathematics.
The instability this has created has me looking to leave academia as quickly as possible; I'm sure others in similar situations are having the same thoughts. This has wreaked havoc on all of academia.
Thank you for providing extra context! I can see why the unpredictability of the entire system could make people not even consider applying in the future.
Sorry to hear that this happened to you. I hope they will provide some way to sort this out soon.
As a professional mathematician, I strongly disagree with the claim that "higher math" abandons worked examples. Any course or book that does not devote a significant amount of time to examples is a bad course or book.
Even Grothendieck, who was famously known for thinking very abstractly and avoiding examples, was motivated by concrete questions (e.g., the Weil conjectures) coming from concrete examples. To me, and most other mathematicians, the whole point of mathematics is to do examples, and theory building or any other abstract nonsense should be motivated by the desire to better understand or unify examples.
