Galileo, one of the founders of modern science, said, "The book of nature is written by the hand of God in the language of mathematics." Paul Dirac, one of the leading figures in twentieth century physics said, "God chose to make the world according to very beautiful mathematics." To any perceptive mind, the mathematical structure of the universe is one of the most compelling evidences of design. Actually, mathematics furnishes four independent lines of evidence.

1. Not only are the basic principles of logic, arithmetic, and algebra true in our universe, but also it is impossible to imagine a universe in which they would not be true. How could there be a universe in which both "A is B" and "A is not B" were true (an example from logic), in which 3 + 5 = 8 (an example from arithmetic), or in which a + b = b + a (an example from algebra)? It would appear that there can be no reality which is not obedient to the basic laws of mathematics. Yet these laws are merely ideas; they have and can have no existence except when they are mentally conceived. Therefore, in the very structure of reality we see evidence of a mind at work. Whose mind if not the mind of God?

2. Even within the constraints of these inviolable laws, you could build a universe in many different ways. Yet, as Dirac said, the blueprint of the universe in which we live is drawn according to very beautiful mathematics. It would not be far-fetched to say that our world is the most mathematical of all possible worlds. In geometry we study the characteristics of space and learn that from a few basic properties of this space we can deduce an elaborate system of informative theorems about geometrical figures—for example, the Pythagorean theorem: c2 = a2 + b2. Perhaps we could imagine a world where this theorem was not true. But it is much more convenient to live in our world, since this theorem gives us a handle on many practical problems. Indeed, modern technology would not be possible except for our ability to find mathematical order wherever we look. The most pervasive and fundamental relations tend to be very simple. Newton's three laws of motion, for example, can be understood by a child. Throughout physics, the basic equations are not difficult: F = ma, W = FD, λ = v/f, E = F/q, E = mc2. What does all this mean? It gives us another proof of the anthropic principle—that the world was evidently made for the sake of man. The mathematical structure of the world makes it easy for man to formulate predictions as to what will happen under stated conditions and on the basis of these predictions to control nature for his own benefit.

Perhaps the most convincing evidence that the world was expressly designed to conform to simple laws that man would readily discover is furnished by the universal law of gravitation: F= Gm1m2/r2. Notice the exponent 2. Why is it not 1.9999999 . . ., or 4.3785264 . . ., or something else hard to use in computations? Yet research has been able to specify the exponent as far as the first six digits, giving 2.00000. Thus, so far as we can tell, the exponent is exactly 2. Coulomb's law of electric force is similar: F = kq1q2/r2. In this case, research has established that the exponent is no different from exactly 2 as far as the first 17 digits. Would we find such laws in an accidental universe?

3. Mathematics furnishes many examples of elegant relationships based on real-world properties, but having no physical meaning or practical value in themselves. The only plausible explanation for such relationships is that God created the world so that its mathematical structure would be a passageway to a much larger structure of abstract mathematics. Why did He adjoin this larger structure to the mathematics of the real world? Because it is His nature to express Himself in things of beauty, and abstract mathematics is a grand symphony, an epic poem, a rich tapestry intelligible to those who are most diligent in thinking God's thoughts after Him. Abstract mathematics is a most puzzling feature of reality if we do not see it as the handiwork of an infinitely clever mind.

Let me give you an example of a relationship discoverable only by abstract math. Never could this be derived from study of the physical universe. In math, three numbers are so important that they are named by letters:

π: ratio of the circumference of a circle to its diameter

e: the number such that ∫exdx = ex + c. In other words, if we were to graph the exponential function ex, the difference between the values of the function at x1 and x2 would equal the area under the curve between those two points.

√-1: Since -1 has no square root, the number is called i, which means "imaginary."

Now watch. When any budding mathematician comes to this equation in the course of his mathematical education, his mouth drops open in sheer wonder and admiration.

e = -1

This equation, a special case of Euler's formula, has been called the most beautiful equation in mathematics. The question raised by this equation is obvious. Though both π and e are concepts well grounded in the real world, their real-world meanings seem totally independent, and i has no real-world meaning whatever. How then can we account for their simple relationship except by invoking a divine mathematician? In this simple equation we perceive the existence of God.

4. Yet we would never perceive the mathematical structure of the universe unless our minds had a knack for mathematics. It is fairly easy for us to grasp the first principles of math and science. These principles are ideas. That is, they are not directly observable in the world about us, nor are they synonymous with any sequence of biochemical events in the brain. Ideas are transphysical. Therefore, the mind which apprehends them cannot be physical in nature. It must belong to another realm, a realm we describe as the realm of the soul. Therefore, man's capacity for mathematics and, more generally, his ability to think are impossible outcomes of organic evolution. His intelligence is the crowning evidence of purpose and design in the universe.

1. All reality must be obedient to laws which are merely ideas.
2. The structure of our universe is mathematical throughout, the most fundamental principles being exceedingly simple.
3. The mathematics of the real world is a bridge to a much larger realm of abstract mathematics.
4. Human beings are capable of mathematical thought.