>this has nothing to do with hard work, and everything to do with the way mathematic is taught. I am a programmer and I would love to understand mathematics the way I understand programming.
How much of your understanding of programming has to do with:
a) teaching/exercises in a class
vs
b) time you've spent hacking on programs, either for a job, or in your spare time
?
Now, how much time have you spent on mathematics compared to time you've spent on programming?
The grandparent's point seems to be that fretting about not having "royal road"[1] is less productive than just spending time working with the ideas.
Good pedagogy can make a difference in how far you get in the time you spend, but there's just not a substitute for putting time in.
How much of your understanding of programming has to do with:
a) teaching/exercises in a class
vs
b) time you've spent hacking on programs, either for a job, or in your spare time
?
Now, how much time have you spent on mathematics compared to time you've spent on programming?
The grandparent's point seems to be that fretting about not having "royal road"[1] is less productive than just spending time working with the ideas.
Good pedagogy can make a difference in how far you get in the time you spend, but there's just not a substitute for putting time in.
--- [1] http://en.wikipedia.org/wiki/Royal_Road#A_metaphorical_.E2.8...