Any One Who Considers Arithmetical Methods Of

I Would Like To Make A Confession Which May Seem Immoral: I Do Not Believe Absolutely In Hilbert Space Any More.

By And Large It Is Uniformly True In Mathematics That There Is A Time Lapse Between A Mathematical Discovery And The Moment When It Is Useful; And That This Lapse Of Time Can Be Anything From 30 To 100 Years, In Some Cases Even More; And That The Whole System Seems To Function Without Any Direction, Without Any Reference To Usefulness, And Without Any Desire To Do Things Which Are Useful.

Technological Possibilities Are Irresistible To Man. If Man Can Go To The Moon, He Will. If He Can Control The Climate, He Will.

It Is Exceptional That One Should Be Able To Acquire The Understanding Of A Process Without Having Previously Acquired A Deep Familiarity With Running It, With Using It, Before One Has Assimilated It In An Instinctive And Empirical Way... Thus Any Discussion Of The Nature Of Intellectual Effort In Any Field Is Difficult, Unless It Presupposes An Easy, Routine Familiarity With That Field. In Mathematics This Limitation Becomes Very Severe.

Any One Who Considers Arithmetical Methods Of Producing Random Digits Is, Of Course, In A State Of Sin.