Drinfeld
===Understand things well===
It's not enough to ''just'' know how to prove a result, or ''just'' have an intuition for it:
the point is not to "get through" a result (and on to the next),
but to understand it deeply. Don't stop when you've "solved" a problem (enough to give a proof):
keep studying it until you understand it well.
This is very much ''my interpretation'' of what he said and implied,
but it has been deeply influential in my thinking and development, mathematical and otherwise,
and is a key cause of my "crisis" in math: if you want to understand everything you know well,
you're in for a very, very long journey.
I feel this is the key point of "Russian mathematics": taking the time to understand things ''well''.
This is quite like Zen Buddhist notions of "quality".
Drinfeld bemoaned peoples' poor knowledge of linear algebra, for instance,
while most mathematicians I know think of it as a class you take after calculus,
and never look back on.
In particular, understand something from several angles, and relate them:
if you have an proof but no intuition, or conversely, or two unrelated proofs,
there's ''a clear gap to fill''.
====X====
That said, it seems some things (particularly new techniques/tricks)
we don't know enough to understand well,
so you just have to (for now!) accept them.
This is very much the "pragmatic" attitude: "Hey, why worry ''why'' it works, just use it!"
(D'apres von Neumann: "You never understand anything in math: you just get used to it.")
===State results suggestively===
Carefully stated results often suggest their own proof.
Don't state results so that the proof is a surprise,
the ideas ''buried'' in the penultimate paragraph of the proof of the second sub-lemma:
place the ideas prominently.
Don't give ''slick'' statements (except perhaps as corollaries):
give ''suggestive'' statements.
There's something deeper here:
some results are "good" results:
the statement corresponds to some structure.
some results are "bad" results:
they are true, but the statement obscures the reason:
they're a consequence of something better,
and are not the right way of thinking about things
A simple example is "all but 1 prime number are odd".
Well, duh.
(other eg from Ani/Apu?)
===Be mneumonic===
After you learn something, you'll forget much of it;
notably, you'll forget technical details.
Try to find or craft something mneumonic to remember.
Yes, of course when studying something technical you'll learn
all the technicalities which you'll soon forget;
the point of a good result or good example is that
''you don't need to know the whole technical apparatus to use/understand this piece''
...and it provides a hook into a mass.
===Simplest non-trivial EG===
as an example,
know the simplest non-trivial EG
(of course know the trivial EGs).
EG, describe the simplest Schur functor that isn't Sym or Alt.
(So it's on ''V^{3}''.)
===Learn to think from a specialists POV===
Something like:
"I want to learn to quack like an algebraic topologist"
The point is to really learn to see the world from
the POV of some other specialist -- not simply taking
a quick statement or result,
but really getting into their mind.
(...and then of course merging it with your own understanding,
yielding deeper understanding)