CHAPTER 1A MYSTERYA few years ago, I was giving a talk at Cornell University. One of my PowerPoint slides read: "Is God a mathematician?" As soon as that slide appeared, I heard a student in the front row gasp: "Oh God, I hope not!"My rhetorical question was neither a philosophical attempt to define God for my audience nor a shrewd scheme to intimidate the math phobics. Rather, I was simply presenting a mystery with which some of the most original minds have struggled for centuries -- the apparent omnipresence and omnipotent powers of mathematics. These are the type of characteristics one normally associates only with a deity. As the British physicist James Jeans (1877-1946) once put it: "The universe appears to have been designed by a pure mathematician." Mathematics appears to be almost too effective in describing and explaining not only the cosmos at large, but even some of the most chaotic of human enterprises.Whether physicists are attempting to formulate theories of the universe, stock market analysts are scratching their heads to predict the next market crash, neurobiologists are constructing models of brain function, or military intelligence statisticians are trying to optimize resource allocation, they are all using mathematics. Furthermore, even though they may be applying formalisms developed in different branches of mathematics, they are still referring to the same global, coherent mathematics.

What is it that gives mathematics such incredible powers? Or, as Einstein once wondered: "How is it possible that mathematics, a product of human thought that isindependent of experience[the emphasis is mine], fits so excellently the objects of physical reality?"This sense of utter bewilderment is not new. Some of the philosophers in ancient Greece, Pythagoras and Plato in particular, were already in awe of the apparent ability of mathematics to shape and guide the universe, while existing, as it seemed, above the powers of humans to alter, direct, or influence it. The English political philosopher Thomas Hobbes (1588-1679) could not hide his admiration either. InLeviathan,Hobbes's impressive exposition of what he regarded as the foundation of society and government, he singled out geometry as the paradigm of rational argument:Seeing then that truth consisteth in the right ordering of names in our affirmations, a man that seeketh precise truth had need to remember what every name he uses stands for, and to place it accordingly; or else he will find himself entangled in words, as a bird in lime twigs; the more he struggles, the more belimed. And therefore in geometry (which is the only science that it hath pleased God hitherto to bestow on mankind), men begin at settling the significations of their words; which settling of significations, they call definitions, and place them in the beginning of their reckoning.Millennia of impressive mathematical research and erudite philosophical speculation have done relatively little to shed light on the enigma of the power of mathematics. If anything, the mystery has in some sense even deepened. Renowned Oxford mathematical physicist Roger Penrose, for instance, now perceives not just a single, but a triple mystery.

Penrose identifies three different "worlds": theworld of our conscious perceptions, the physical world,and thePlatonic world of mathematical forms.The first world is the home of all of our mental images -- how we perceive the faces of our children, how we enjoy a breathtaking sunset, or how we react to the horrifying images of war. This is also the world that contains love, jealousy, and prejudices, as well as our perception of music, of the smells of food, and of fear. The second world is the one we normally refer to as physical reality. Real flowers, aspirin tablets, white clouds, and jet airplanes reside in this world, as do galaxies, planets, atoms, baboon he.