Les Faits Ne Parlent Pas. Facts Do

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.

Mathematics Is The Art Of Giving The Same Name To Different Things. [as Opposed To The Quotation: Poetry Is The Art Of Giving Different Names To The Same Thing].

Intuition Is More Important To Discovery Than Logic.

Thus, Be It Understood, To Demonstrate A Theorem, It Is Neither Necessary Nor Even Advantageous To Know What It Means.

It Is Through Science That We Prove, But Through Intuition That We Discover.