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Thu Jun 18 15:39:13 CEST 2009

How to do math?

(At least, what works for me?)

1. The human brain abstracts from examples, not the other way around.
   Do not attempt to go too far without doing active manipulations
   (exercise!).  Mathematics is not a spectator sport.

2. Try to intuitively understand the basic concepts (definitions).  If
   they are too abstract this means that you don't understand well
   enough the theory which _suggests_ these abstractions.  Usually new
   definitions come from patterns that cannot be properly abstracted
   in some basic theory, but making the theory more abstract usually
   does expose the patterns.

3. Look at the most important theorems.  Try to understand how they
   work intuitively, then (very important!) look at the proofs, or at
   least the core elements.

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