You Don't Have To Be Responsible For

Truth Is Much Too Complicated To Allow Anything But Approximations.

If One Has Really Technically Penetrated A Subject, Things That Previously Seemed In Complete Contrast, Might Be Purely Mathematical Transformations Of Each Other.

Kurt Godel's Achievement In Modern Logic Is Singular And Monumental - Indeed It Is More Than A Monument, It Is A Landmark Which Will Remain Visible Far In Space And Time. ... The Subject Of Logic Has Certainly Completely Changed Its Nature And Possibilities With Godel's Achievement.

Neumann, To A Physicist Seeking Help With A Difficult Problem: Simple. This Can Be Solved By Using The Method Of Characteristics. Physicist: I'm Afraid I Don't Understand The Method Of Characteristics. Neumann: In Mathematics You Don't Understand Things. You Just Get Used To Them.

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.