Mathematical Visualization Quotes

Evolution has ensured that our brains just aren't equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it's just as easy to think in 11 dimensions, as it is to think in three or four.

Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

Strange! I don't understand how it is that we can write mathematical expressions and calculate what the thing is going to do without being able to picture it.

It is here [in mathematics] that the artist has the fullest scope of his imagination.

I see a certain order in the universe and math is one way of making it visible.

In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture.

Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.

Squaring numbers is a symmetrical process that I like very much. And when I divide one number by another, say, 13 divided by 97, I see a spiral rotating downwards in larger and larger loops that seem to warp and curve. The shapes coalesce into the right number. I never write anything down.

Grandad taught me that the alien signs and symbols of algebraic equations were not just marks on paper. They were not flat. They were three-dimensional, and you could approach them from different directions, look at them from different ways, stand them on their heads. You could take them apart and put them back together in a variety of shapes, like Legos. I stopped being scared of them.

The essential fact is that all the pictures which science now draws of nature, and which alone seem capable of according with observational facts, are mathematical pictures.

In the mind's eye, a fractal is a way of seeing infinity.

Some mathematicians didn't even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.