Quote by Hermann Weyl

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of…

— David Hilbert

We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth…

— Hans Reichenbach

“an impossible geometry”

— Alessandro Baricco

“We must here follow the first course so as to be able to pass on later to generalisations which extend beyond the limits of…

— Hermann Weyl

“It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as…

— Bernhard Riemann

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for,…

— Carl Friedrich Gauss

Axiomatization is what one does last, it's rubbish. It's the hygiene of mathematics, axiomatization.

— Serge Lang

We cannot ... prove geometrical truths by arithmetic.

— Aristotle

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for,…

— Carl Friedrich Gauss

“Even a pure mathematician may find his appreciation of this geometry [applied geometry] quickened, since there is no mathematician so pure that he feels…

— G.H. Hardy

Every writer must reconcile, as best he may, the conflicting claims of consistency and variety, of rigour in detail and elegance in the whole.…

— Julian Coolidge

One geometry cannot be more true than another; it can only be more convenient.

— Henri Poincare