Mathematics Is Not A Contemplative But A

It Is Rather Astonishing How Little Practical Value Scientific Knowledge Has For Ordinary Men, How Dull And Commonplace Such Of It As Has Value Is, And How Its Value Seems Almost To Vary Inversely To Its Reputed Utility.

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.

I Have Never Done Anything 'useful'. 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... Judged By All Practical Standards, The Value Of My Mathematical Life Is Nil; And Outside Mathematics It Is Trivial Anyhow. I Have Just One Chance Of Escaping A Verdict Of Complete Triviality, That I May Be Judged To Have Created Something Worth Creating. And That I Have Created Something Is Undeniable: The Question Is About Its Value.

No One Has Yet Discovered Any Warlike Purpose To Be Served By The Theory Of Numbers Or Relativity, And It Seems Unlikely That Anyone Will Do So For Many Years.

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