Chess Problems Are The Hymn-tunes Of Mathematics.

I Believe That Mathematical Reality Lies Outside Us, That Our Function Is To Discover Or Observe It, And That The Theorems Which We Prove, And Which We Describe Grandiloquently As Our "creations," Are Simply The Notes Of Our Observations.

In [great Mathematics] There Is A Very High Degree Of Unexpectedness, Combined With Inevitability And Economy.

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.

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.

Mathematics Is Not A Contemplative But A Creative Subject; No One Can Draw Much Consolation From It When He Has Lost The Power Or The Desire To Create; And That Is Apt To Happen To A Mathematician Rather Soon. It Is A Pity, But In That Case He Does Not Matter A Great Deal Anyhow, And It Would Be Silly To Bother About Him.