Mathematical Discoveries, Small Or Great Are Never

Mathematicians Do Not Deal In Objects, But In Relations Between Objects; Thus, They Are Free To Replace Some Objects By Others So Long As The Relations Remain Unchanged. Content To Them Is Irrelevant: They Are Interested In Form Only.

When The Physicists Ask Us For The Solution Of A Problem, It Is Not Drudgery That They Impose On Us, On The Contrary, It Is Us Who Owe Them Thanks.

Mathematics Is The Art Of Giving The Same Name To Different Things.

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.

Science Is Built Up With Facts, As A House Is With Stones. But A Collection Of Facts Is No More A Science Than A Heap Of Stones Is A House.