I'll admit that i take this a little personally, but what does this mean, "oustide of academia"? Where do you think an interest in advanced mathematics lives? Your complaint, on its face, seems to be that everyone interested enough to be doing advanced mathematics is employed doing it?
Do you mean to say that advanced mathematics has no practical use outside of making more mathematics?
I think what you will find is that the mathematicians have trouble extracting their benefit to society, given that mathematics is fundamentally not subject to copyright. We're happy to contribute as long as we get to eat something and, for the most part, we get to decide what we work on.
This is a pretty fucking good trade, since just about every problem offers some kind of insight into some other problem, and we're just an interested lot, so probably someone has spent a lot of time thinking about the problem that you're specifically interested in.
I don't think your complaint is coherent enough to really be argued against, unfortunately, as I would like to change your mind, so would you mind making more sense?
You see that here on HN with all the articles on Category Theory. CT appeals to people who majored in Comp Sci but long for some advanced and abstract mathematics to get away from the daily dose of Node. It is simplistic enough that you can read the first few chapters of a CT book and feel like you're really getting some deep math topics.
This is a set. This is a mapping. This is a set of sets. This is a mapping from elements to elements. This is a mapping from elements to sets. This is a mapping from sets to sets. This is the inverse mapping…. Chapter after chapter.
But then there’s “insight” that all of mathematics can be cast as CT, because… all math is just things that map to things! Whoa, far out, dude. Mind is blown.
However, I'm glad I did the PhD.
The 4 years I spent on it were time in my life well spent. I enjoyed the work and it didn't bother me to be earning less than I otherwise would have.
The main skill I gained from the PhD was being able to read technical papers - typically involving stats or financial math. I have needed to do this on and off for my work, and I've found that lots of people who have good high school or college math find this much much harder than I do.
I study math for fun. I find the ability to do this precious and life affirming. When I read an interesting article in Quanta, I can look at the papers cited, if it's a field I have some background in, and make more sense of them than the average reader. In ten years of doing this, I have once published a short paper which added a small improvement to a recreational problem. So studying math isn't really about external achievement - I am the equivalent of someone who plays the guitar at home but will never have a gig or record a song. But I feel very lucky to exist in a time period when I had access to this educational opportunity, and when so much interesting math is available to read and study essentially for free.
Being disconnected to reality is a feature in pure math.