Aspect Quote by Hans Reichenbach

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

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

We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be…

— Hans Reichenbach

A geometrical theory in physical interpretation can never be validated with mathematical certainty ... ; like any other theory of empirical science, it can…

— Carl Gustav Hempel

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

Now ... the basic principle of modern mathematics is to achieve a complete fusion [of] 'geometric' and 'analytic' ideas.

— Jean Dieudonne

“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

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

— Henri Poincare

The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of…

— David Berlinski

Certainly it is permitted to anyone to put forward whatever hypotheses he wishes, and to develop the logical consequences contained in those hypotheses. But…

— Giuseppe Peano

“an impossible geometry”

— Alessandro Baricco