Mathematics student here. How much effort do my math/sci/bros put into learning new mathematics.
I have come to believe that almost no one is born with the ability to use complex mathematical reasoning, and that anyone who wishes to be able to do so must supply the utmost effort.
I don't consider it "effort" to sit down with a Springer book and a cup of coffee and read about some Grothendiecks ideas for an hour a day. It's like watching a sitcom with one eye and eventually you understand the plot anyhow. Disclaimer: I don't do proofs for a living.
How do you define "complex mathematical reasoning"? I read in a MathOverflow answer by Tao that at one point he was rolling on the floor when thinking about about some wave PDE's and I think in pictures too.
Complex mathematical reasoning can have many definitions. We could base it on average understanding of math, which gives us some idea of simple mathematical reasoning.
However, this would mean anything above calculus (in developed countries, arithmetic in undeveloped) would be complex, which to anyone in STEM is complete hogwash. So lets say mathematics that requires vigor, such as: proofing mathematics, analysis. I'm talking about things that are more than plug and chug problem solving.
Something like this for me as well; it depends how you define effort.
I study math because I like math. In that sense there isn't really effort involved, any more than there's effort involved in sitting down and playing a video game.
But on the other hand, of course mathematics is difficult to understand. You have to really try to understand it, and even if you're very talented you get stuck a lot.
So there's effort there, but there's also that same kind of effort at getting good at StarCraft or whatever game you play.
I don't really agree with the term "rigorous practice."
I don't sit down and say "okay gotta drill the shit out of these exercises.", and I don't really think that's a good way to do things (in my own opinion, anyway).
It's just playing around with new ideas and problems.
It's cultural/familial. Asians are good at math because their society demands it. People who grow up with scientists and mathematicians for parents are going to excel at those things. Hard work will go a very long way, and exceptionally good or bad luck can obviously make you a genius or an imbecile, but it's fundamentally about the environment you're raised in. That is my honest belief.
Citation: I am a community college student so clearly I know these things.