Begin With The Simplest Examples.

Galileo Was No Idiot. Only An Idiot Could Believe That Science Requires Martyrdom - That May Be Necessary In Religion, But In Time A Scientific Result Will Establish Itself.

A Mathematical Problem Should Be Difficult In Order To Entice Us, Yet Not Completely Inaccessible, Lest It Mock At Our Efforts. It Should Be To Us A Guide Post On The Mazy Paths To Hidden Truths, And Ultimately A Reminder Of Our Pleasure In The Successful Solution.

In Mathematics ... We Find Two Tendencies Present. On The One Hand, The Tendency Towards Abstraction Seeks To Crystallise The Logical Relations Inherent In The Maze Of Materials ... Being Studied, And To Correlate The Material In A Systematic And Orderly Manner. On The Other Hand, The Tendency Towards Intuitive Understanding Fosters A More Immediate Grasp Of The Objects One Studies, A Live Rapport With Them, So To Speak, Which Stresses The Concrete Meaning Of Their Relations.

I Have Tried To Avoid Long Numerical Computations, Thereby Following Riemann's Postulate That Proofs Should Be Given Through Ideas And Not Voluminous Computations.

The Art Of Doing Mathematics Consists In Finding That Special Case Which Contains All The Germs Of Generality.