For Any Serious Purpose, Intelligence Is A

Young Men Should Prove Theorems, Old Men Should Write Books.

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.

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.

I Remember Once Going To See Him [ramanujan] When He Was Lying Ill At Putney. I Had Ridden In Taxi-cab No. 1729, And Remarked That The Number Seemed To Me Rather A Dull One, And That I Hoped It Was Not An Unfavourable Omen. "no," He Replied, "it Is A Very Interesting Number; It Is The Smallest Number Expressible As A Sum Of Two Cubes In Two Different Ways."

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.