There is no royal road to 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