For Any Serious Purpose, Intelligence

The Theory Of Numbers, More Than Any Other Branch Of Mathematics, Began By Being An Experimental Science. Its Most Famous Theorems Have All Been Conjectured, Sometimes A Hundred Years Or More Before They Were Proved; And They Have Been Suggested By The Evidence Of A Mass Of Computations.

No Mathematician Should Ever Allow Him To Forget That Mathematics, More Than Any Other Art Or Science, Is A Young Man's Game. ... Galois Died At Twenty-one, Abel At Twenty-seven, Ramanujan At Thirty-three, Riemann At Forty. There Have Been Men Who Have Done Great Work Later; ... [but] I Do Not Know Of A Single Instance Of A Major Mathematical Advance Initiated By A Man Past Fifty. ... A Mathematician May Still Be Competent Enough At Sixty, But It Is Useless To Expect Him To Have Original Ideas.

For Any Serious Purpose, Intelligence Is A Very Minor Gift.

... Philosophy Proper Is A Subject, On The One Hand So Hopelessly Obscure, On The Other So Astonishingly Elementary, That There Knowledge Hardly Counts.

I Remember Once Going To See Him [ramanujan] When He Was Lying Ill At Putney. I Had Ridden In Taxi-cab No. 1729, And Remarked That The Number Seemed To Me Rather A Dull One, And That I Hoped It Was Not An Unfavourable Omen. "no," He Replied, "it Is A Very Interesting Number; It Is The Smallest Number Expressible As A Sum Of Two Cubes In Two Different Ways."