For My Part, It Is Difficult For

I Count Maxwell And Einstein, Eddington And Dirac, Among "real" Mathematicians. The Great Modern Achievements Of Applied Mathematics Have Been In Relativity And Quantum Mechanics, And These Subjects Are At Present At Any Rate, Almost As "useless" As The Theory Of Numbers.

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.

A Science Or An Art May Be Said To Be "useful" If Its Development Increases, Even Indirectly, The Material Well-being And Comfort Of Men, It Promotes Happiness, Using That Word In A Crude And Commonplace Way.

Archimedes Will Be Remembered When Aeschylus Is Forgotten, Because Languages Die And Mathematical Ideas Do Not. "immortality" May Be A Silly Word, But Probably A Mathematician Has The Best Chance Of Whatever It May Mean.

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.