As History Proves Abundantly, Mathematical

Reductio Ad Absurdum, Which Euclid Loved So Much, Is One Of A Mathematician's Finest Weapons. It Is A Far Finer Gambit Than Any Chess Play: A Chess Player May Offer The Sacrifice Of A Pawn Or Even A Piece, But A Mathematician Offers The Game.

Exposition, Criticism, Appreciation, Is Work For Second-rate Minds.

It Is A Melancholy Experience For A Professional Mathematician To Find Himself Writing About Mathematics. The Function Of A Mathematician Is To Do Something, To Prove New Theorems, To Add To Mathematics, And Not To Talk About What He Or Other Mathematicians Have Done. Statesmen Despise Publicists, Painters Despise Art-critics, And Physiologists, Physicists, Or Mathematicians Have Usually Similar Feelings: There Is No Scorn More Profound, Or On The Whole More Justifiable, Than That Of The Men Who Make For The Men Who Explain. Exposition, Criticism, Appreciation, Is Work For Second-rate Minds.

Perhaps Five Or Even Ten Per Cent Of Men Can Do Something Rather Well. It Is A Tiny Minority Who Can Do Anything Really Well, And The Number Of Men Who Can Do Two Things Well Is Negligible. If A Man Has Any Genuine Talent, He Should Be Ready To Make Almost Any Sacrifice In Order To Cultivate It To The Full.

... Philosophy Proper Is A Subject, On The One Hand So Hopelessly Obscure, On The Other So Astonishingly Elementary, That There Knowledge Hardly Counts.