Challenges Quote by Benoit Mandelbrot

The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the…

— Benoit Mandelbrot

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

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the…

— Benoit Mandelbrot

In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet…

— Nikolai Lobachevsky

“No very good sense can be given to the idea that the elements of Euclidean geometry may be found in nature because either everything…

— David Berlinski

The early study of Euclid made me a hater of geometry.

— James Joseph Sylvester

For each successive class of phenomena, a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate…

— Henry John Stephen Smith

There are no forms in nature. Nature is a vast, chaotic collection of shapes. You as an artist create configurations out of chaos. You…

— Ansel Adams

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

I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without…

— Benoit Mandelbrot

We live in a world populated by structures - a complex mixture of geological, biological, social, and linguistic constructions that are nothing but accumulations…

— Manuel De Landa

Geometry is the archetype of the beauty of the world.

— Johannes Kepler