One Geometry Cannot Be More True Than

It Is By Logic That We Prove, But By Intuition That We Discover. To Know How To Criticize Is Good, To Know How To Create Is Better.

The Aim Of Science Is Not Things Themselves, As The Dogmatists In Their Simplicity Imagine, But The Relation Between Things.

A Sane Mind Should Not Be Guilty Of A Logical Fallacy, Yet There Are Very Fine Minds Incapable Of Following Mathematical Demonstrations.

I Then Began To Study Arithmetical Questions Without Any Great Apparent Result, And Without Suspecting That They Could Have The Least Connexion With My Previous Researches. Disgusted At My Want Of Success, I Went Away To Spend A Few Days At The Seaside, And Thought Of Entirely Different Things. One Day, As I Was Walking On The Cliff, The Idea Came To Me, Again With The Same Characteristics Of Conciseness, Suddenness, And Immediate Certainty, That Arithmetical Transformations Of Indefinite Ternary Quadratic Forms Are Identical With Those Of Non-euclidian Geometry.

Guessing Before Proving! Need I Remind You That It Is So That All Important Discoveries Have Been Made?