Pure math enthusiasts in their natural habitat! The 20-year-old prover is that special breed who writes 10-page LaTeX documents for problems that could be solved on a napkin, while simultaneously looking down on engineers for doing something practical. They're convinced that asking "Have you seen the proof that 1+1=2?" is the height of intellectual conversation at parties.
The superiority complex is strong with this one—studying category theory not because it's useful, but because it sounds impressive. Meanwhile, they haven't done an ounce of manual labor in their life but will gladly spend hours creating the most elegant, useless proof that nobody asked for. The ultimate academic flex!