Projective geometry is all geometry.

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

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

— Henri Poincare

Geometry existed before creation.

— Plato

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 is the most complete science.

— David Hilbert

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

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

— Vladimir Arnold

“This relationship, often called the Golden mean, has been discovered and rediscovered at various times in history as a unique proportion believed to have…

— John Pile

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

— Plato

“A circle has no end.”

— Isaac Asimov

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

In order to give meaning to the world, one has to feel oneself involved in what he frames. This attitude requires concentration, a discipline…

— Henri Cartier-Bresson

While fractal geometry is often used in high-tech science, its patterns are surprisingly common in traditional African designs.

— Ron Eglash

The geometry reveals five development direction for applications (each with endless possibilities); dividing, dwelling, trestle, fenestration and artistic installation. I find these enabled designs…

— Dror Benshetrit

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

— Nicholas Murray Butler