It Is With Logic That One Proves;

A Sane Mind Should Not Be Guilty Of A Logical Fallacy, Yet There Are Very Fine Minds Incapable Of Following Mathematical Demonstrations.

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.

In One Word, To Draw The Rule From Experience, One Must Generalize; This Is A Necessity That Imposes Itself On The Most Circumspect Observer.

Need We Add That Mathematicians Themselves Are Not Infallible?

Later Generations Will Regard Mengenlehre (set Theory) As A Disease From Which One Has Recovered.