(January 2, 2016 at 1:09 pm)Jörmungandr Wrote: A large part of math is training your brain how to think properly. There is no substitute for doing the work.
I never did the work because I was bright enough to pass the tests without doing the work. I would just absorb the concepts and improvise the supporting bridges.
For example, I never worked through the trigonometric identities. So even in Differential Equations, if I needed a bit of trigonometry, I would invent it on the hoof from sin^2 x + cos^2 x = 1. This basically doomed my later math career.
I suggest you do the work.
Knowing how to derive these things is incredibly important, too, but when push comes to shove, even when you for example do cutting edge research, *anything* you know by heart will allow you to think faster about things. It will make the difference of being able to complete a complicated argument at the blackboard vs. awkwardly scrambling for notes for half a day. Some things you only see in the first place if youhave done the work. I say that as someone who like you tended to be lazy with the rote work, compensating by deriving on the fly.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition
