zyklu5

Indeed. In fact, it is one of the most amusing aspect of the anglophone west (at least for the last few decades). Despite public perception (by public I mean those who have been to university since the 90s), Western historians of science and mathematics in general have never not acknowledged the previous works of the Persianate civilizations commensurate to their knowledge of them in their time. But somehow in the last few decades professional historians have had to waste time figuratively looking over their shoulders lest they be percieved as being Eurocentric. And, if they were to somehow find a way to show -- requiring whatever hermeneutical gymnastics -- that a prominent scientist was influenced (or even better, had stolen) from some other "cultures" than nothing better! (ex: Copernicus from the Maragha school as an example of interpretive gymnastics)

But, of course, this is one of the symptoms of the degeneration that now afflicts your particular civilization and is bringing about it's inevitable transformation to something else -- but better this than the fate of the Abassids or the Sung.

On the contrary, what is presented by the OP is one of the many reasons that worship of science's heroes, unfashionable for decades, a whiggish pablum, is justified. If great results were birthed fully-formed -- a view I've frankly never heard anyone profess who has bothered to consider such things even briefly -- they would hardly be any heroes. Even little children who reflexively chomp on every superhero film aeroplaned towards their face understand this.

If I'm being honest I really don't have a good recommendation for a text in intro abstract algebra. I learned it from Michael Artin's Algebra. Artin is a true master -- along with David Mumford, he was the main apostle for Grothendieck style AG in the US -- but his book was not very easy to learn from.

There is indeed a deep connection between what is going on behind Arnold's proof and the classical Galois theory. But it needs quite a bit of sophistication to flesh out properly (not apparent in his famous lectures given to high school kids). There is a Galois theory for Riemann surfaces over algebraic functions where the coverings behave like fields do in the classical correspondence. If any one is interested, check out chapter 3 of Khovanskii's Galois Theory, Coverings and Riemann Surfaces.

You know how in every zombie movie there's a bit where our intrepid protagonists must blend in to avoid capture. I think this is that sort of thing.

Atiyah is truly one of the giants of modern mathematics. I remember long ago I struggled through a reading course of his and Bott's Yang-Mills paper in graduate school. Like many great works of math it too had that paradoxical characteristic of transforming seemingly 'non-mathematics' into mathematics* by reversing the usual direction of application of one to the other, in this case, from physics to math. It would start a whole movement that'll produce much of modern geometries greatest hits like Donaldson's (his student) theorem in 4 manifolds to Witten's great papers.

* A reason I think modern LLM architecture as they currently stand with their underlying attention mechanisms will not produce interesting new mathematics. A few other ideas are going to be needed.

And why should I simply assume that "Education Economists"* really know the subject they purport to talk about? Because they are credentialed members of university departments with some label? Because a few of them won some Bank of Sweden award?

Just because a particular department or field of study exists in academia does not magically give them the imprimatur you think it does.

* Btw, I know for a fact that a few of them are not "education economists"