The Elastic Fractal – digital image by Noel Giffin. Fractals are generated with statistical rules for “self similarity”.

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Everyone knows that if you want to do physics or engineering, you had better be good at mathematics. More and more people are finding out that if you want to work in certain areas of economics or biology, you had better brush up on your mathematics. Mathematics has penetrated sociology, psychology, medicine, and linguistics. Under the name of cliometry, it has been infiltrating the field of history, much to the shock of old-timers. Why is this so? What gives mathematics its power? What makes it work?
    One very popular answer has been that God is a Mathematician. If, like Laplace, you don’t think that deity is a necessary hypothesis, you can put it this way: the universe expresses itself naturally in the language of mathematics. The force of gravity diminishes as the second power of the distance; the planets go around the sun in ellipses; light travels in a straight line, or so it was thought before Einstein. Mathematics, in this view, has evolved precisely as a symbolic counterpart of the universe. It is no wonder, then, that mathematics works; that is exactly its reason for existence. The universe has imposed mathematics upon humanity.

Davis, Philip J. & Hersh, Reuben. The Mathematical Experience, Birkhauser 1981, (back cover)