The Total Subject Of Mathematics Is Clearly

The Calculus Was The First Achievement Of Modern Mathematics And It Is Difficult To Overestimate Its Importance. I Think It Defines More Unequivocally Than Anything Else The Inception Of Modern Mathematics; And The System Of Mathematical Analysis, Which Is Its Logical Development, Still Constitutes The Greatest Technical Advance In Exact Thinking.

The Total Subject Of Mathematics Is Clearly Too Broad For Any Of Us. I Do Not Think That Any Mathematician Since Gauss Has Covered It Uniformly And Fully; Even Hilbert Did Not And All Of Us Are Of Considerably Lesser Width Quite Apart From The Question Of Depth Than Hilbert.

The Sciences Do Not Try To Explain, They Hardly Even Try To Interpret, They Mainly Make Models. By A Model Is Meant A Mathematical Construct Which, With The Addition Of Certain Verbal Interpretations, Describes Observed Phenomena. The Justification Of Such A Mathematical Construct Is Solely And Precisely That It Is Expected To Work-that Is, Correctly To Describe Phenomena From A Reasonably Wide Area.

With Four Parameters I Can Fit An Elephant, And With Five I Can Make Him Wiggle His Trunk.

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.