Fermat's Engima

The last few days I've be captivated by the book 'Fermat's Enigma' written by Simon Singh. It has been a journey into the depths of what the mathematicans world thinks. Here are a few snippets from the book to set you thinking -

Everything is Number
-Pythagoras

Immortality may be a silly word, but probably a mathematician has the best chance of whatever it may mean.
-GH Hardy

God exists since mathematics is consistent. Devil exists since we cannot prove it.
-Andre Weil

Basically it's just a matter of thinking. Often you write something down to clarify your thoughts, but not necessarily. In particular when you've reached a real impasse, when there's a real problem that you want to overcome, then the routine kind of mathematical thinking is of no use to you. Leading up to that kind of new idea there has to be a long period of tremendous focus on the problem without any distraction. You have to really think about that problem - just concentrate on it. Then you stop. Afterwards there seems to be a kind of period of relaxation during which the subconscious appears to take over and it's during that time that some new insight comes.
-Andrew Wiles