Mathematicians are chronically lost and confused 
Secondary math education, for me in the UK, didn't deal with anything outside of elementary algebra, Euclidean geometry, some statistics, and relatively simple calculus. Nobody talked to us about imaginary or complex numbers, or bayes theorem, decision theory, or non-trivial mechanics problems until I was in college (age 16+). Nobody mentioned matrices, broader number theory or discrete transforms until I was in university. I studied EE not compsci. Things like algorithmic complexity I had to learn for myself and from Knuth. I'm trying to grok group theory right now to help with my understanding of crypto. Before this, it was never mentioned throughout my education, so I don't know what courses you would have had to take to learn that. The fact that I didn't even know group theory was important to crypto until after I had made the choice strikes me as a bad sign.<p>The common theme at every level is learning cherry-picked skills, before you're even <i>told what the branches of mathematics even are</i>. Everything seems disjointed because you're not taught to look past the trees for the forest. Most people infact, even technical folk, go through their entire lives without knowing the forest even exists. Any idiot can point to a random part of their anatomy and posit that there's a field of study dedicated to it. The same goes for mechanics or computer science. You just can't do that with mathematics as a student.<p>I loath academic papers. Often I find I spend days or weeks deciphering mathematics in compsci papers only to find the underlying concept is intuitive and plain, but you're forced to learn it bottom up, constructing the authors original genius from the cryptic scrawlings they left in their paper... and you realise a couple of block diagrams and a few short paragraphs could have made the process a lot less frustrating.<p>So many ideas seem closed to mortals because of the nature of mathematics.