A Man Who Sets Out

Good Work Is No Done By "humble" Men. It Is One Of The First Duties Of A Professor, For Example, In Any Subject, To Exaggerate A Little Both The Importance Of His Subject And His Own Importance In It. A Man Who Is Always Asking "is What I Do Worth While?" And "am I The Right Person To Do It?" Will Always Be Ineffective Himself And A Discouragement To Others. He Must Shut His Eyes A Little And Think A Little More Of His Subject And Himself Than They Deserve. This Is Not Too Difficult: It Is Harder Not To Make His Subject And Himself Ridiculous By Shutting His Eyes Too Tightly.

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.

It Is A Melancholy Experience For A Professional Mathematician To Find Himself Writing About Mathematics. The Function Of A Mathematician Is To Do Something, To Prove New Theorems, To Add To Mathematics, And Not To Talk About What He Or Other Mathematicians Have Done. Statesmen Despise Publicists, Painters Despise Art-critics, And Physiologists, Physicists, Or Mathematicians Have Usually Similar Feelings: There Is No Scorn More Profound, Or On The Whole More Justifiable, Than That Of The Men Who Make For The Men Who Explain. Exposition, Criticism, Appreciation, Is Work For Second-rate Minds.

No Mathematician Should Ever Allow Him To Forget That Mathematics, More Than Any Other Art Or Science, Is A Young Man's Game. ... Galois Died At Twenty-one, Abel At Twenty-seven, Ramanujan At Thirty-three, Riemann At Forty. There Have Been Men Who Have Done Great Work Later; ... [but] I Do Not Know Of A Single Instance Of A Major Mathematical Advance Initiated By A Man Past Fifty. ... A Mathematician May Still Be Competent Enough At Sixty, But It Is Useless To Expect Him To Have Original Ideas.

For Any Serious Purpose, Intelligence Is A Very Minor Gift.