There Are No Solved Problems;

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.

We Also Know How Cruel The Truth Often Is, And We Wonder Whether Delusion Is Not More Consoling.

The Task Of The Educator Is To Make The Child's Spirit Pass Again Where Its Forefathers Have Gone, Moving Rapidly Through Certain Stages But Suppressing None Of Them. In This Regard, The History Of Science Must Be Our Guide.

Every Good Mathematician Should Also Be A Good Chess Player And Vice Versa.

Geometry Is The Art Of Correct Reasoning From Incorrectly Drawn Figures.