Every Mathematical Discipline Goes Through Three Periods

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.

If One Were To Bring Ten Of The Wisest Men In The World Together And Ask Them What Was The Most Stupid Thing In Existence, They Would Not Be Able To Discover Anything So Stupid As Astrology.

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.

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.

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