Mathematics Is A Game Played According To

Geometry, Like Arithmetic, Requires For Its Logical Development Only A Small Number Of Simple, Fundamental Principles. These Fundamental Principles Are Called The Axioms Of Geometry.

Before Beginning [to Try To Prove Fermat's Last Theorem] I Should Have To Put In Three Years Of Intensive Study, And I Haven't That Much Time To Squander On A Probable Failure.

The Tool Which Serves As Intermediary Between Theory And Practice, Between Thought And Observation, Is Mathematics; It Is Mathematics Which Builds The Linking Bridges And Gives The Ever More Reliable Forms.

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.

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.