In The Old Days When People Invented

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.

When The Logician Has Resolved Each Demonstration Into A Host Of Elementary Operations, All Of Them Correct, He Will Not Yet Be In Possession Of The Whole Reality, That Indefinable Something That Constitutes The Unity ... Now Pure Logic Cannot Give Us This View Of The Whole; It Is To Intuition That We Must Look For It.

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.

Just As Houses Are Made Of Stones, So Is Science Made Of Facts.

For A Long Time The Objects That Mathematicians Dealt With Were Mostly Ill-defined; One Believed One Knew Them, But One Represented Them With The Senses And Imagination; But One Had But A Rough Picture And Not A Precise Idea On Which Reasoning Could Take Hold.