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One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.

The image is more than an idea. It is a vortex or cluster of fused ideas and is endowed with energy.

All of imagination - everything that we think, we feel, we sense - comes through the human brain. And once we create new patterns in this brain, once we shape the brain in a new way, it never returns to its original shape.

My big thesis is that although the world looks messy and chaotic, if you translate it into the world of numbers and shapes, patterns emerge and you start to understand why things are the way they are.

I have been a multitude of shapes, Before I assumed a consistent form.

Among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other, and continues to fascinate me, is the structure hidden in mathematical things.

A number of images put together a certain way become something quite above and beyond what any of them are individually.

Real shapes and real patterns are things you would observe in nature, like the marks on the back of a cobra's hood or the markings on a fish or a lizard. Imaginary shapes are just that, symbols that come to a person in dreams or reveries and are charged with meaning.

It's kind of like trying to make straight lines from curves, but involving shapes that sort of dictate what the curves are, if you like, and the difference between two separate pieces creates a third transitional piece if you like.

When something is beautiful in math, everything is just perfectly lined up, and you see through sheer thought that something really beautiful can take place.