Geometry Is Not True, It

Often When Works At A Hard Question, Nothing Good Is Accomplished At The First Attack. Then One Takes A Rest, Long Or Short, And Sits Down Anew To The Work. During The First Half-hour, As Before, Nothing Is Found, And Then All Of A Sudden The Decisive Idea Presents Itself To The Mind.

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.

It Is Not Order Only, But Unexpected Order, That Has Value.

Doubt Everything Or Believe Everything: These Are Two Equally Convenient Strategies. With Either We Dispense With The Need For Reflection.

Mathematicians Do Not Study Objects, But Relations Among Objects; They Are Indifferent To The Replacement Of Objects By Others As Long The Relations Don't Change. Matter Is Not Important, Only Form Interests Them.