Abstract

Gallileo described the universe in his most famous line: "This grand book is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures." Why should the laws of nature be subject to statement in such elegantly basic algebra? Why does gravity work by the principle of inverse squares? Why do simple geometrics pervade nature--from the hexagons of the honeycomb, to the complex architecture of crystals? D'Arcy Thompson, author of Growth and Form and my earliest intellectual hero (along with my father and Charles Darwin), wrote that "the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of math ematical beauty." Many scientists, if only to coin a striking metaphor, depict a creating God as a mathematician from the realm of Plato or Pythagoras. The physicist James Jeans wrote: "From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.".