Evidence of Design in Mathematics


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." 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" are 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 Paul Dirac, one of the leading figures in twentieth century physics, 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 with 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 to date has certified that at least the first five digits after 2 are 0's. 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 at least the first 17 digits of the exponent are no different from exactly 2. Would we find such laws in an accidental universe?

3. Mathematics furnishes many examples of elegant relationships based in some measure on real-world properties but beyond the reach of mere science. The only plausible explanation for such relationships is that God created the physical universe so that its structure would be a passageway to the much larger structure of abstract mathematics. Why did He adjoin this larger structure to observable reality? 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. To explain why the domains of truth include abstract mathematics is impossible unless we see it as the handiwork of an infinitely clever mind.

Let me give you an example of a relationship discoverable only by abstract mathematics. 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.)

i: same as √-1 (The number is called i, which means "imaginary," because -1 has no square root.)


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.


eiπ = -1


This equation, a special case of Euler's formula, has been declared the most beautiful in mathematics. The question that it raises is obvious. Though π, e, and -1 are concepts grounded in the real world, their real-world meanings imply no interconnection, and i has no real-world meaning whatever. How then can we account for this profound equation bringing them all together except by invoking a divine mathematician? Just in one simple mathematical sentence we can see the hand of God.

4. We would remain blind to the mathematical structure of the universe if our minds had no aptitude for mathematics. But to grasp its first principles is, for most people, fairly easy. 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 spirit. 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.

In summary, mathematics furnishes three steps of evidence leading to certainty that the world must have been created by God.

  1. Throughout the structure of our universe, we see conformity to mathematical laws.
  2. The mathematics governing the real world is a bridge to the much larger realm of abstract mathematics.
  3. All mathematics, whether or not it refers to things concrete, exists only in a mind.

Therefore, the prominent place of mathematics both in the design of the physical world and in the world of human thought proves that the universe must have been conceived and created by a Great Mind: namely, God.


Evidence of Design in Natural Law


We can reach the same conclusion by reformulating our argument to emphasize science rather than mathematics. As we stated earlier, one remarkable feature of the natural world is that all of its phenomena obey relatively simple laws. The scientific enterprise exists because man has discovered that wherever he probes nature, he finds laws shaping its operation.

If all natural events have always been lawful, we must presume that the laws came first. How could it be otherwise? How could the whole world of nature have ever precisely obeyed laws that did not yet exist? But where did they exist? A law is simply an idea, and an idea exists only in someone's mind. Since there is no mind in nature, nature itself must be unconscious of the laws governing it.

Modern science takes it for granted that the universe has always danced to rhythms it cannot hear, but still assigns power of motion to the dancers themselves. How is that possible? The power to make things happen in obedience to universal laws cannot reside in anything ignorant of these laws.

Would it be more reasonable to suppose that this power resides in the laws themselves? Of course not. Ideas have no intrinsic power. They affect events only as they direct the will of a thinking person. Only a thinking person has the power to make things happen. Since natural events were lawful before man ever conceived of natural laws and since, in any case, he is far too weak to enforce his will on the world around him, the thinking person responsible for the orderly operation of the universe must be a higher Being, a Being we know as God.

A famous defender of evolution in recent years was Carl Sagan. Yet before he died he admitted that one thing he could not explain was natural law.