You can't criticize geometry. It's never wrong.

Leibniz is at the disadvantage of not having seen it. Or perhaps we should count this as an advantage, for anyone who sees it…

— Neal Stephenson

Geometry is knowledge of the eternally existent.

— Pythagoras

Geometry is one of the handles of science and philosophy.

— Xenocrates

The science of the church is neglected for the study of geometry, and they lose sight of Heaven while they are employed in measuring…

— Edward Gibbon

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

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method

— Nicholas Murray Butler

I have an infamously low capacity for visualizing relationships, which made the study of geometry and all subjects derived from it impossible for me.

— Sigmund Freud

Let no-one ignorant of geometry enter. Said to have been inscribed above the door of Plato's Academy.

— Plato

Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.

— Vladimir Arnold

No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the 'square root'…

— Michael Atiyah

Geometry is the most complete science.

— David Hilbert

Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities,…

— Benoit Mandelbrot

Geometry existed before creation.

— Plato

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most…

— Henri Poincare

Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine…

— Jean le Rond d'Alembert