He Who Seeks For Methods Without Having

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.

Mathematical Science Is In My Opinion An Indivisible Whole, An Organism Whose Vitality Is Conditioned Upon The Connection Of Its Parts.

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.

Galileo Was No Idiot. Only An Idiot Could Believe That Science Requires Martyrdom - That May Be Necessary In Religion, But In Time A Scientific Result Will Establish Itself.

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.