But For Harmony Beautiful To Contemplate, Science

How Is Error Possible In Mathematics?

It Is The Harmony Of The Diverse Parts, Their Symmetry, Their Happy Balance; In A Word It Is All That Introduces Order, All That Gives Unity, That Permits Us To See Clearly And To Comprehend At Once Both The Ensemble And The Details.

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.

The Scientist Does Not Study Nature Because It Is Useful To Do So. He Studies It Because He Takes Pleasure In It, And He Takes Pleasure In It Because It Is Beautiful. If Nature Were Not Beautiful It Would Not Be Worth Knowing, And Life Would Not Be Worth Living. I Am Not Speaking, Of Course, Of The Beauty Which Strikes The Senses, Of The Beauty Of Qualities And Appearances. I Am Far From Despising This, But It Has Nothing To Do With Science. What I Mean Is That More Intimate Beauty Which Comes From The Harmonious Order Of Its Parts, And Which A Pure Intelligence Can Grasp.

Ideas Rose In Clouds; I Felt Them Collide Until Pairs Interlocked, So To Speak, Making A Stable Combination.