A great example of a mathematics popularizer along these lines is Norman Wildberger, who has an astonishing range of videos on youtube about an amazing range of mathematical topics. Here’s an interview with him: https://youtu.be/E_dGqavx5AU .
My personal feeling is that a lot of beautiful and interesting mathematics will arise as a result of an intuitionist, finitist, computationalist rethinking of the foundations of mathematics.
Just kidding. But seriously, ZFC is probably the easiest foundation you can have for proper mathematics. Anything else is more complicated (if you think otherwise, you probably just don't understand it).
E.g. https://mitpress.mit.edu/books/functional-differential-geome...
The Lisp code in this book is truly not doing anything for me. Seems like a kind of direct numerical computation/translation. I actually think it would be better to do it in Haskell which seems like it would at least let you identify some more generic structures (oh we can actually implement this idea x as a functor/monad blah blah).
I think this is the basis for the enthusiasm, almost entirely. There's a growing perception that a lot of mathematical abstractions that are purely naval-gazing have arisen from ZFC, and the intuitionalists and finitists are gaining followers amongst amateur and upcoming mathematicians. I don't have data to back this, just a feeling that I get.
And I think in particular this is attractive to programmers because this skews closer to what we've learned about computability and program design, and I think there's even some hope of moving forward from obscure notation and single-letter variable names towards a syntax for doing mathematics that can be more expressive and easier to verify.