As Littlewood Said To Me Once [of

No Discovery Of Mine Has Made, Or Is Likely To Make, Directly Or Indirectly, For Good Or Ill, The Least Difference To The Amenity Of The World.

Real Mathematics Must Be Justified As Art If It Can Be Justified At All.

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.

As History Proves Abundantly, Mathematical Achievement, Whatever Its Intrinsic Worth, Is The Most Enduring Of All.

A Science Or An Art May Be Said To Be "useful" If Its Development Increases, Even Indirectly, The Material Well-being And Comfort Of Men, It Promotes Happiness, Using That Word In A Crude And Commonplace Way.