Being an engineer by training, I never got exposed to much algebra in my courses (beyond the usual high school stuff in high school). In fact did not miss it much either. Tried to learn some algebraic geometry then... oh the horror. For whatever reason, my intuition is very geometric and analytic (in the calculus sense). Even things like counting and combinatorics, they feel weird, like dry flavorless pretzels made of dried husk. Combinatorics is good only when I can use Calculus. Calculus, oh that's different, it's rich savoury umami buttery briskets. Yum.

That's not the interesting part. The interesting part is that I thought everyone is the same, like me.

It was a big and surprising revelation that people love counting or algebra in just the same way I feel about geometry (not the finite kind) and feel awkward in the kind of mathematics that I like.

It's part of the reason I don't at all get the hate that school Calculus gets. It's so intuitive and beautifully geometric, what's not to like. .. that's usually my first reaction. Usually followed by disappointment and sadness -- oh no they are contemplating about throwing such a beautiful part away.

"The Axiom of Choice is obviously true, the Well-ordering theorem obviously false, and who can tell about Zorn's lemma?"

(attributed to Jerry Bona)

The complex numbers are just elements of R[i]/(i^2+1). I don't even understand how people are able to get this wrong.

Hah. This perspective is how you get an embedding of booleans into the reals in which False is 1 and True is -1 :-)

(Yes, mathematicians really use it. It makes parity a simpler polynomial than the normal assignment).

Obviously.