'The Unreasonable Effectiveness of Mathematics in the Natural Sciences'

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. -- Eugene Wigner

Read Wigner's whole article, 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences'. (You can also download a PDF copy of the article and read its Wikipedia entry.) Wigner brings up the tremendous question of why mathematics, which was mostly developed independently of application, does such a marvelous job of describing the physical world? It is a deeply profound question if you stop to contemplate it, both from a scientific and theological perspective.

The short theological answer is that mathematics illuminates the underlying beauty of the structure of creation. While I strongly support this point of view, it still leaves the original question largely unanswered. Why is the universe able to be understood in a manner comprehensible by man? And why by tools that were not originally developed to do so?

Einstein himself was baffled by this:

The most incomprehensible thing about the universe is that it is comprehensible. -- Albert Einstein

How can it be that mathematics, being after all product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? -- Albert Einstein.

There is absolutely no question that math does a wonderful job of modeling the natural world. It is not without limitations, but the deeper we delve into the mathematical world, the deeper we are able to delve into the physical. Virtually all of physics, most of engineering, much of chemistry, and increasingly biology rests on mathematical application and understanding. It is quite amazing that this should be so.

Most of economic growth, whether it be from increases in agricultural production, computer technology, the continued advancement of transportation (air, land, and sea), advances in statistics and quality control, accounting and financial innovations, the evolving of venture capital and expansion of credit markets, etc., has math as a critical part of its foundation. Without the discovery of math, mankind would have never advanced to where it is today.

A much less settled question is how effective and appropriate mathematics is for modeling the social sciences. I'll save that discussion for another day...