Mathematics Has A Threefold Purpose. It Must

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.

Absolute Space, That Is To Say, The Mark To Which It Would Be Necessary To Refer The Earth To Know Whether It Really Moves, Has No Objective Existence.... The Two Propositions: "the Earth Turns Round" And "it Is More Convenient To Suppose The Earth Turns Round" Have The Same Meaning; There Is Nothing More In The One Than In The Other.

In The Old Days When People Invented A New Function They Had Something Useful In Mind. Now, They Invent Them Deliberately Just To Invalidate Our Ancestors' Reasoning, And That Is All They Are Ever Going To Get Out Of Them.

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.

A Scientist Worthy Of His Name, About All A Mathematician, Experiences In His Work The Same Impression As An Artist; His Pleasure Is As Great And Of The Same Nature.