I think there is absolutely nothing in math one should memorize. "In abstract algebra failing memorize might kill you" is nonsense. Memorize what? Axioms of group? Tactics that can be applied to problems?
please consider the statement from the position of a student just learning the material (like the OP). if you are working through a book with 1000+ problems, like pinter (as some people are suggesting), and you have to keep looking up stuff like how to verify a subgroup, how long is that book going to take you?
to me, memorization means to recall the important parts of something accurately and precisely so that they can be used fluently. that is not to say textually (rote memorization). i do not think it is enough to say "well, that's what learning is" because i doubt most people learn most things to that level.
