Well said. Memorizing the API is fundamental to success in most branches of math - but this erects a barrier that a lot of able individuals are unable to cross. I've always thought this was a problem but I almost never hear of anybody complaining about this so I figured it was just me. Languishing in the established system is usually interpreted as "sour grapes".
It strikes me as a collective means for mathematicians to reduce entry into their field and thus to increase their own salaries. Maybe you don't have to get a "math license" to practice math, but you have to somehow acquire a huge body of knowledge that is almost never spelled out fully in the mathematics literature. This will prevent many people from becoming mathematicians and thus make math a more exclusive and lucrative endeavor.
To be cynical about it.
I guess that's not much different from most fields' use of specialized vocabulary, etc. There are many informal methods of dissuading people from competing in your own little corner of the labor market.
