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Mercury, January/February 2003 Table of Contents

Courtesy of Christine Klicka (STScI), inspired by William Blake's painting The Ancient of Days.

by Mario Livio

For some inexplicable reason, mathematics does an extraordinary job of explaining the universe.

Many outstanding physicists, most notably Albert Einstein, Eugene Wigner, and James Jeans, remarked that mathematics appears to be just too effective in explaining the universe. Wigner, in particular, wrote a remarkable paper in 1960 titled "The Unreasonable Effectiveness of Mathematics in the Physical Sciences." He wrote, "The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."

We may wonder, for example, why all the phenomena encompassed by electromagnetism, from the behavior of electrons to the nature of light, can be explained by a set of four differential equations known as Maxwell's equations. Equally puzzling is the fact that some geometrical curves like the ellipse, invented/discovered by the Greek mathematician Menaechmus around 350 BC, were found 2,000 years later to describe the orbits of planets around the Sun. Similarly, group theory proved to be essential in the understanding of both the organization of elementary (subatomic) particles, and the structure of solids. What is it that makes mathematics fit the observable universe like a glove?

The attempts to answer this question fall generally into two broad categories. According to one view, mathematics is in some sense the actual "language" of the universe. It exists independent of us humans, and we are merely discovering it in the workings of the cosmos. Proponents of this philosophy like to point out that even some of the more esoteric areas of mathematics, such as non-Euclidean geometries, were eventually found to provide cornerstones to cosmological models.