Mathematics May, Like Poetry Or Music, "promote

No Discovery Of Mine Has Made, Or Is Likely To Make, Directly Or Indirectly, For Good Or Ill, The Least Difference To The Amenity Of The World.

No Mathematician Should Ever Allow Himself To Forget That Mathematics, More Than Any Other Art Or Science, Is A Young Man's Game

Mathematics Is Not A Contemplative But A Creative Subject; No One Can Draw Much Consolation From It When He Has Lost The Power Or The Desire To Create; And That Is Apt To Happen To A Mathematician Rather Soon. It Is A Pity, But In That Case He Does Not Matter A Great Deal Anyhow, And It Would Be Silly To Bother About Him.

The Mathematician's Patterns, Like The Painter's Or The Poet's, Must Be Beautiful.

Pure Mathematics Is On The Whole Distinctly More Useful Than Applied... For What Is Useful Above All Is Technique, And Mathematical Technique Is Taught Mainly Through Pure Mathematics.