Young Men Should Prove Theorems, Old Men

Mathematics May, Like Poetry Or Music, "promote And Sustain A Lofty Habit Of Mind."

Most People Have Some Appreciation Of Mathematics, Just As Most People Can Enjoy A Pleasant Tune; And There Are Probably More People Really Interested In Mathematics Than In Music. Appearances Suggest The Contrary, But There Are Easy Explanations. Music Can Be Used To Stimulate Mass Emotion, While Mathematics Cannot; And Musical Incapacity Is Recognized (no Doubt Rightly) As Mildly Discreditable, Whereas Most People Are So Frightened Of The Name Of Mathematics That They Are Ready, Quite Unaffectedly, To Exaggerate Their Own Mathematical Stupidity

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."

Real Mathematics Must Be Justified As Art If It Can Be Justified At All.

The Mathematician's Patterns, Like The Painter's Or The Poet's Must Be Beautiful; The Ideas, Like The Colours Or The Words Must Fit Together In A Harmonious Way. Beauty Is The First Test: There Is No Permanent Place In The World For Ugly Mathematics.