A Small Error In The Former Will

Most Striking At First Is The Appearance Of Sudden Illumination, A Manifest Sign Of Long Unconscious Prior Work.

The Task Of The Educator Is To Make The Child's Spirit Pass Again Where Its Forefathers Have Gone, Moving Rapidly Through Certain Stages But Suppressing None Of Them. In This Regard, The History Of Science Must Be Our Guide.

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].

Consider Now The Milky Way. Here Also We See An Innumerable Dust, Only The Grains Of This Dust Are No Longer Atoms But Stars; These Grains Also Move With Great Velocities, They Act At A Distance One Upon Another, But This Action Is So Slight At Great Distances That Their Trajectories Are Rectilineal; Nevertheless, From Time To Time, Two Of Them May Come Near Enough Together To Be Deviated From Their Course, Like A Comet That Passed Too Close To Jupiter. In A Word, In The Eyes Of A Giant, To Whom Our Suns Were What Our Atoms Are To Us, The Milky Way Would Only Look Like A Bubble Of Gas.

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.