Thought Is Only A Flash Between Two

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.

There Are No Solved Problems; There Are Only Problems That Are More Or Less Solved.

I Entered An Omnibus To Go To Some Place Or Other. At That Moment When I Put My Foot On The Step The Idea Came To Me, Without Anything In My Former Thoughts Seeming To Have Paved The Way For It, That The Transformations I Had Used To Define The Fuchsian Functions Were Identical With Non-euclidean Geometry.

It Is Often Said That Experiments Should Be Made Without Preconceived Ideas. That Is Impossible. Not Only Would It Make Every Experiment Fruitless, But Even If We Wished To Do So, It Could Not Be Done. Every Man Has His Own Conception Of The World, And This He Cannot So Easily Lay Aside. We Must, Example, Use Language, And Our Language Is Necessarily Steeped In Preconceived Ideas. Only They Are Unconscious Preconceived Ideas, Which Are A Thousand Times The Most Dangerous Of All.

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