The "seriousness" Of A Mathematical Theorem Lies,

Chess Problems Are The Hymn-tunes Of Mathematics.

When The World Is Mad, A Mathematician May Find In Mathematics An Incomparable Anodyne. For Mathematics Is, Of All The Arts And Sciences, The Most Austere And The Most Remote, And A Mathematician Should Be Of All Men The One Who Can Most Easily Take Refuge Where, As Bertrand Russell Says, "one At Least Of Our Nobler Impulses Can Best Escape From The Dreary Exile Of The Actual World."

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 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.

In [great Mathematics] There Is A Very High Degree Of Unexpectedness, Combined With Inevitability And Economy.