Chess Problems Are The Hymn-tunes Of Mathematics.

A Science Is Said To Be Useful If Its Development Tends To Accentuate The Existing Inequalities In The Distribution Of Wealth, Or More Directly Promotes The Destruction Of Human Life.

A Chess Problem Is Genuine Mathematics, But It Is In Some Way "trivial" Mathematics. However, Ingenious And Intricate, However Original And Surprising The Moves, There Is Something Essential Lacking. Chess Problems Are Unimportant. The Best Mathematics Is Serious As Well As Beautiful-"important" If You Like, But The Word Is Very Ambiguous, And "serious" Expresses What I Mean Much Better.

It Is Hardly Possible To Maintain Seriously That The Evil Done By Science Is Not Altogether Outweighed By The Good. For Example, If Ten Million Lives Were Lost In Every War, The Net Effect Of Science Would Still Have Been To Increase The Average Length Of Life.

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.

There Is Always More In One Of Ramanujan's Formulae Than Meets The Eye, As Anyone Who Sets To Work To Verify Those Which Look The Easiest Will Soon Discover. In Some The Interest Lies Very Deep, In Others Comparatively Near The Surface; But There Is Not One Which Is Not Curious And Entertaining.