Looking from the outside in, serious mathematics seems to require a ton of memorization. I really don't know how they keep all the names of everything straight,

Looking from the outside in, serious mathematics seems to require a ton of memorization. I really don't know how they keep all the names of everything straight, and what they mean, and how they relate to one another, and so on. That's all memory. There also seems to be an awful lot of drilled pattern recognition (as in you've gotta have the pattern and what it means when you see it memorized) in both the reading and writing of proofs. From where I sit the mountains between me and deep mathematical understanding sure look like they're mostly memorization and drilling until various identities and mechanical operations are second-nature. Some of those peaks are surely "ah ha" moments or creative thinking or whatever but... not most of it. Maybe on the far side, but I can't even see that far. And damn is that far side ever removed from what 99% of people need math for. Not the way a literature class might be, but the way a Latin or Attic Greek language class might be. It's that far off and round-about and well into diminishing-returns territory.