I'm speaking from experience. It's a generational gap, I think, which is why it's hard to understand. But it's true.
FA is using cosines up and down the spectrum to convert a set of samples (audio, image, etc) into a frequency spectrum (the magnitude associated with each cosine).
I didn't have to look that up. I just know it. And I'm no genius. This isn't nearly as difficult as it seems.
Especially because universities usually spoonfeed you information at an absurdly slow rate. There's value in that – I'd wager you could whip me if we have to bust out some paper and solve some integrals. But then again, I can just get a computer to do that hard work for me. I know what integrals mean and why they're useful, which is far more important than the rote memorization of techniques to solve them.
Now, if you want to argue that there are specializations that you can only learn in university, you'll get no disagreement from me. Distributed systems is a perfect example. On the other hand, I know those fundamentals too because I completed 6.824 on my own time. It's freely available.
And yeah, matrix math is a piece of cake too.
The world has simply changed. Information used to be valuable and guarded. Now all that matters is raw talent and motivation.
And credentials, sadly. But the world is slowly learning those aren't a great proxy for talent.
It's probably hard to empathize because you were well off enough to go to university. But you have to remember that intelligence is mostly genetic (probably), so talent can come from all walks of life. What would you have done if your parents had a massive divorce and someone squandered what little your family had? Are you sure you would have gotten a scholarship? When your parents never instilled the value of university into you from a young age?