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Pure Mathematics Is On The Whole Distinctly More Useful Than Applied... For What Is Useful Above All Is Technique, And Mathematical Technique Is Taught Mainly Through Pure Mathematics.

If A Man Is In Any Sense A Real Mathematician, Then It Is A Hundred To One That His Mathematics Will Be Far Better Than Anything Else He Can Do, And That He Would Be Silly If He Surrendered Any Decent Opportunity Of Exercising His One Talent In Order To Do Undistinguished Work In Other Fields. Such A Sacrifice Could Be Justified Only By Economic Necessity Of Age.

No Mathematician Should Ever Allow Himself To Forget That Mathematics, More Than Any Other Art Or Science, Is A Young Man's Game

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.

A Mathematician, Like A Painter Or Poet, Is A Maker Of Patterns. If His Patterns Are More Permanent Than Theirs, It Is Because They Are Made With Ideas.