If Nature Were Not Beautiful, It Would

It Is Through Science That We Prove, But Through Intuition That We Discover.

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.

Hypotheses Are What We Lack The Least.

. . . By Natural Selection Our Mind Has Adapted Itself To The Conditions Of The External World. It Has Adopted The Geometry Most Advantageous To The Species Or, In Other Words, The Most Convenient. Geometry Is Not True, It Is Advantageous.

The Mathematical Facts Worthy Of Being Studied Are Those Which, By Their Analogy With Other Facts, Are Capable Of Leading Us To The Knowledge Of A Physical Law. They Reveal The Kinship Between Other Facts, Long Known, But Wrongly Believed To Be Strangers To One Another.