The Mind Uses Its Faculty

Every Phenomenon, However Trifling It Be, Has A Cause, And A Mind Infinitely Powerful, And Infinitely Well-informed Concerning The Laws Of Nature Could Have Foreseen It From The Beginning Of The Ages. If A Being With Such A Mind Existed, We Could Play No Game Of Chance With Him; We Should Always Lose.

Talk With M. Hermite. He Never Evokes A Concrete Image, Yet You Soon Perceive That The More Abstract Entities Are To Him Like Living Creatures.

It Is The Simple Hypotheses Of Which One Must Be Most Wary; Because These Are The Ones That Have The Most Chances Of Passing Unnoticed.

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.

Thought Is Only A Flash Between Two Long Nights, But This Flash Is Everything.