Bombs Are Probably More Merciful Than Bayonets

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.

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.

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.

The Creative Life Was The Only One For A Serious Man.

A Mathematician ... Has No Material To Work With But Ideas, And So His Patterns Are Likely To Last Longer, Since Ideas Wear Less With Time Than Words.