We often hear that Mathematics consists mainly in "proving theorems". Is a writer's job mainly in writing sentences?
A mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks.
To master mathematics is to master an intangible view, it is to acquire the skill of a virtuoso who cannot pin his performance on criteria.
By Gian-Carlo Rota on "The Mathematical Experience" by Philip J.Davis and Reuben Hersh