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?
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.