If Nature Were Not Beautiful,

The Advance Of Science Is Not Comparable To The Changes Of A City, Where Old Edifices Are Pitilessly Torn Down To Give Place To New, But To The Continuous Evolution Of Zoologic Types Which Develop Ceaselessly And End By Becoming Unrecognisable To The Common Sight, But Where An Expert Eye Finds Always Traces Of The Prior Work Of The Centuries Past. One Must Not Think Then That The Old-fashioned Theories Have Been Sterile And Vain.

Thus, Be It Understood, To Demonstrate A Theorem, It Is Neither Necessary Nor Even Advantageous To Know What It Means. The Geometer Might Be Replaced By The "logic Piano" Imagined By Stanley Jevons; Or, If You Choose, A Machine Might Be Imagined Where The Assumptions Were Put In At One End, While The Theorems Came Out At The Other, Like The Legendary Chicago Machine Where The Pigs Go In Alive And Come Out Transformed Into Hams And Sausages. No More Than These Machines Need The Mathematician Know What He Does.

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

Thought Must Never Submit, Neither To A Dogma, Nor To A Party, Nor To A Passion, Nor To An Interest, Nor To A Preconceived Idea, Nor To Whatever It May Be, Save To The Facts Themselves, Because, For Thought, Submission Would Mean Ceasing To Be.

Mathematicians Do Not Study Objects, But Relations Among Objects; They Are Indifferent To The Replacement Of Objects By Others As Long The Relations Don't Change. Matter Is Not Important, Only Form Interests Them.