One of the biggest critiques I had about mathematical proofs is that they are so darn hard to understand.  I want the author to walk me through how they arrived at the correct answer.  Perhaps the proof would teach me something meaningful about theorem or I would arrive at some better understanding.  But there are a great deal of very unenlightening proofs out there.  The proofs I’m talking about usually beautiful structure and clever mathematics which ends in a flourish or a bang when the theorem is proved.  But I have no idea how they came to that conclusion.

You too may find this to be true about math. (or perhaps this is why you hated geometry in high school?) I used to think bitter thoughts about some author’s proofs. Then my real analysis professor said something fascinating.  I think he may have been quoting someone else (any one out there know who he was quoting?).  A masterpiece of architecture would never be opened to the public with it’s scaffolding still up.  You are to see the final product and wonder at it’s beauty as apposed to analyzing how it was built.  For the same reason mathematicians remove the scaffolding from their proofs once they are complete.  They do the final finish work and publish incomprehensible and beautiful proofs.

So the next time you read a mathematical argument and find it incompressible- I challenge you to look for beauty in the proof.  If you can see a glimmer of charm in that proof, then the author has achieved his goal of a beautiful, elegant proof.