^ This. I ended up majoring in pure mathematics as an undergraduate after finding out that applied mathematics courses had too much material to memorize after finding out that physics courses had too much material to memorize. Pure math was so much easier.
You and the person who started this thread seem to think that way. I find there is just as much to memorize in math. fields, rings, groups, and all sorts of things. Oh and those greek letters. I like math and physics and stuff but I never thought there was significantly less memorization in math. Calc 2 techniques of integration and then DiffEq seemed like a lot of special cases that had unique solutions we had to remember.
Each of those is just a definition and a handful (literally like 5 or 6) of axioms. If I memorized the axioms and a few key theorems I could usually derive everything else in the homework and on the exams. Most mathematical objects have very similar structure and the rest is just maps (morphisms) between them.
> Oh and those greek letters.
That's actually a very valid point. It took me a few years after graduating to realize how much myself (and I suspect many other students) are hampered by not knowing the notation well enough. Most people just assume you (and they) know what it means and never think about the actual definition and ambiguities. Even not being able to pronounce Greek letters definitely makes you less able (or at least less confident) to reason with them.
> Calc 2 techniques of integration and then DiffEq seemed like a lot of special cases that had unique solutions we had to remember.
That's the applied math part of calculus. The pure side is just "here's a compact/open/whatever set, prove for any point in it this property holds." Then you find out no one cares about either and it's all just numerical algorithms.
