[Computational Complexity] Putting the Pieces Together
A student proves what I feel is quite a nice result but the student laments that the proof was easy, they had simply put together various tools from earlier papers. Guess what? That's called research. Every mathematical result is simply of combination of logical statements put together in the right way. But unless P=NP we cannot automate this process. Our job is to figure out how to combine results and techniques we already know to prove things we didn't know before.
Most proofs seem simple once we've proved them. With some notable exceptions, every proof has (at most) one new idea, the rest just connecting the dots through techniques we've seen before.
From the outside or from the eyes of a young graduate students, research seems like a magical process that mathematicians somehow pull proofs out of a hat. Successful theorists are not magicians, just people who have read and understood techniques from a variety of sources and find news ways to put those techniques together to solve the problem on hand.
Posted by Lance to Computational Complexity at 9/13/2006 05:37:00 AM