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Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
The application of algebra to geometry ... has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.
The science [geometry] is pursued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes.
Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.
We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.
In terms of individuals who actually inspired me, very few of the academic people that I had access to had that power over me. Maybe it's simply because I wasn't that committed to geometry.
Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of geometry consists in these sense qualities.
In order to give meaning to the world, one has to feel oneself involved in what he frames. This attitude requires concentration, a discipline of mind, sensitivity, and a sense of geometry.
I call it sacred geometry. When everything's just right and it feels really balanced, so that when it unfolds to the next part, you feel totally familiar and at ease within the song.
I'd been doing projects outdoors for the public. I made pigeons eat geometry by putting bread out in rhomboids and triangles. I don't know if this activity made sense, but the work was available.