Consequence Quote by Giuseppe Peano

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

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 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

“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

Geometry is the science of correct reasoning on incorrect figures.

— George Polya

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 is the rules of all mental investigation

— Mikhail Lomonosov

For it is the duty of an astronomer to compose the history of the celestial motions or hypotheses about them. Since he cannot in…

— Andreas Osiander

We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.

— Ludwig Wittgenstein

Geometry is knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them.

— Rudolf Steiner

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

Geometry is the only science that it hath pleased God hitherto to bestow on mankind.

— Thomas Hobbes