The Art Of Doing Mathematics

Geometry, Like Arithmetic, Requires For Its Logical Development Only A Small Number Of Simple, Fundamental Principles. These Fundamental Principles Are Called The Axioms Of Geometry.

Mathematics Is A Presuppositionless Science. To Found It I Do Not Need God, As Does Kronecker, Or The Assumption Of A Special Faculty Of Our Understanding Attuned To The Principle Of Mathematical Induction, As Does Poincaré, Or The Primal Intuition Of Brouwer, Or, Finally, As Do Russell And Whitehead, Axioms Of Infinity, Reducibility, Or Completeness, Which In Fact Are Actual, Contentual Assumptions That Cannot Be Compensated For By Consistency Proofs.

One Can Measure The Importance Of A Scientific Work By The Number Of Earlier Publications Rendered Superfluous By It

However Unapproachable These Problems May Seem To Us And However Helpless We Stand Before Them, We Have, Nevertheless, The Firm Conviction That Their Solution Must Follow By A Finite Number Of Purely Logical Processes.

The Art Of Doing Mathematics Consists In Finding That Special Case Which Contains All The Germs Of Generality.