Real Mathematics Must Be Justified As Art

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.

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.

If I Could Prove By Logic That You Would Die In Five Minutes, I Should Be Sorry You Were Going To Die, But My Sorrow Would Be Very Much Mitigated By Pleasure In The Proof.

A Person’s First Duty, A Young Person’s At Any Rate, Is To Be Ambitious, And The Noblest Ambition Is That Of Leaving Behind Something Of Permanent Value.

Chess Problems Are The Hymn-tunes Of Mathematics.