Can God be Proved…by Mathematics?
by Edward W. Ng
“The theist sees enough evidence and does not need proof of God, whereas the atheist will never be satisfied by any proof.”
The beauty of math to connote reverence for God often shows up on chain emails, such as patterns derived from Pascal’s Triangle [a triangle of numbers in which a row represents the coefficients of the binomialbseries]. The kind of beauty and symmetry appearing in Pascal’s triangle has over the years generated many philosophical questions: Are mathematical patterns inherent in nature to be discovered, or simply smart inventions of human minds to create patterns out of a random nature?
Interestingly, Pascal, one of the most famous Christian mathematicians, always carried a prayer reminder in the lining of his coat that read: “Complete submission to Jesus Christ and to my Director; eternally in joy for a day’s exercise on Earth. May I not forget Thy words. Amen.” (Ref 2)
Mathematics and Reality
Math is used commonly in our daily lives—in counting money, planning time, listening to weather forecasts. Two main schools of thought about math have emerged, historically. One school considers math a tool primarily, to be used for the study of nature and the advancement of other human endeavors such as engineering and construction. Examples in this school of thought are Newton, who discovered calculus as a tool to support his exploration of nature; Galileo, who believed that math is the language used by God to describe His works and thus it behooves humans to learn that language; and Descartes, who later reinforced these ideas. (Ref 3)
The other school of thought, held by G. Hardy and B. Russell, looks at math as an end in itself, exploring or inventing the logical beauty and self consistency for human enjoyment－ analogous to music. (Ref 4) This view can be illustrated by a musical example. Beethoven wrote his symphonies with an aim at musical structure, expression, and beauty— for enjoyment as an end in itself. (Ref 5) However, over the ages his music has become applicable in many other human spheres of activity. In the movie The King’s Speech, at the climatic speech of the finale, Beethoven’s 7th Symphony brought the climax to a higher level, which underscored the many psychosocial struggles the King had to endure.
Critical to these considerations is whether mathematics is the product of a higher intelligence for humans to discover, or is it purely a human invention. In both Western and Eastern philosophies, the ancient sages have long recognized the existence of a concrete physical reality and an abstract perceptual reality. The natural alignment of the two schools mentioned above really converges to, on one side, a theistic view of mathematics imbedded in natural order to be discovered, while, on the other, an atheistic view that nature evolved at random, serving as a marvelous laboratory for humans to invent patterns to explore it.
There is, however, a possible third reality which compounds these two views. Plato suggested a reality of mathematical perfection outside of the perceptual and physical realities. (Ref 6) He believed that the kinds of geometric or number patterns which we see, either in our invention, or in nature, are merely shadows of something that is perfect. For the theist, this third, perfect abstract reality is easy to fit into his worldview—as part of the Divine reality. For the atheist, he is not able to accept perfection which is not directly observable. However, he is stuck with a puzzlement of how and why there is such order and design hidden in nature.
Efforts to Prove God
Several top mathematicians have attempted to use logic or mathematics to prove the existence of God. Newton summarized best in the form of a question, “Whence arises all that order and beauty we see in the universe?” (Ref 7) Leibinitz applied rigor to a cosmological proof of God—the idea based on the argument that every event has a cause, and therefore there must be a first cause of everything. This ultimate cause would naturally be God. The atheistic logician B. Russell, used the origin of the human race as an example to mock this proof. (Ref 8) But if asked to explain the origin, he had to resort to mother nature, which in his mind came from random evolution. Randomness cannot explain much of design and order in nature, nor does it answer Newton’s fundamental question cited above.
In the community of mathematical logic, there is the well-known “Godel’s ontological proof” of the existence of God. The idea of the proof may be summarized this way. In human’s perceptual reality, there exists the concept of perfect goodness, which logically must come from some higher entity. (Ref 9) For those who are unwilling to acknowledge a higher entity: Can the ontological concept of perfection evolve from a one-cell micro-organism, even as the evolutionists want to believe? Can they come up with a mathematical proof, or prove by experiment or observation?
Godel’s Ontological Proof was, of course, controversial. It basically was applying modern mathematical logic in the realm of metaphysics. B. Russell, Godel’s contemporary, could not come up with a counter proof, which is a classic example of a famous saying by Immanuel Kant that it is hard to prove the existence of God, but even harder to prove His non-existence. (Ref 10) Logician H. Wang, in his reflections on his mentor Godel, reminisced that the latter advised him to ponder on three big philosophical topics: free will, God, and eternal destiny. Wang, an agnostic, said that he was simply not interested in such questions. (Ref 11) Unfortunately many, like Wang, have chosen not to follow the words of Jesus, “Seek and ye shall find” (Matthew 7:7).
Is God a Mathematician?
From the days of St. Augustine, there have been mathematicians who used numerology to manipulate people and predict all kinds of events. Some Christians have claimed calculations in the Bible to predict the end of time. These people misuse both mathematics and the Bible, and give both a bad name. The pastor who calculated from the Bible the Lord’s return on May 21, 2011, generated a lot of news and was ridiculed by the media. Augustine warned: “Good Christians should beware of mathematicians, and all those who make empty prophesies.” (Ref 12)
In Newton’s era, mathematicians tried to understand the beauty in nature’s design as the handiwork of God. Newton, perhaps the most famous “creation scientist,” and respected in the science community as one of the greatest mathematicians and top physicists of all ages, was motivated to discover calculus as a language to describe motion, and to understand the Divine nature through a clearer understanding of physical nature and reality. He accepted the Bible and had no problem with Genesis 1. (Ref 13)
Two of Newton’s predecessors, G. Galileo and J. Kepler, both believed in the existence of design in nature to be discovered. Galileo was explicit that “God is a mathematician and thus we find mathematical properties in nature.” (Ref 14) Kepler expressed similar sentiments this way: “The Christian knows that the mathematical principles, according to which the corporeal world was to be created, are coeternal with God. Geometry has supplied God with the models for the creation of the world. Within the image of God, it has passed into man, and was certainly not received within through eyes.” (Ref 15)
Other great mathematicians had a similar theistic view of nature, familiar names such as Descartes, Leibritz, Euler, Gauss, Riemann, and the previously mentioned Pascal. Pascal had a humorous way to advise people to think about God and eternal destiny. He said, “If a believer dies and there is no God, the person loses nothing; but if there is God, he has gained heaven, while his skeptics lose everything in hell.”
Natural ly there are great mathematicians on both sides of the faith divide. The phenomenon of agnosticism and atheism has become more pronounced as science entered the 20th century, and has been used to promote a form of scientism, greatly extrapolating the reaches of science. B. Russell was famous for his stand. When asked by a friend what he would say if one day he faced God, Russell said, “I’d raise my fist to him and ask, ‘Why didn’t you give me sufficient information to believe you?’” (Ref 16) Another British mathematician G. H. Hardy once listed a New Year wish, “to find argument for the nonexistence of God.” (Ref 17)
God in His Heaven
In the study of the cosmos, there are two aspects of mathematics that hold the key to understanding any theoretical structure. On the one hand, there are the equations and formulae which are central to any paradigm in physical sciences. But on the other hand, there are some fundamental constants, that is, special numbers that hold the key to applicability of these equations. In his book Accidental Universe, (Ref 18) mathematical physicist P. Davies listed 25 fundamental constants as the key elements that would constitute any physical structures in the cosmos, such as solar system, galaxies or clusters of galaxies. If any of these constants varies very slightly, the solar system could not have evolved to its present form, and thus the human race would not have existed.
God-phobia or Worship
In the intellectual world, despite compelling evidence of design in nature, unfortunately many worship a form of scientism and simply cannot accept the concept of a higher intelligence above nature. So they insist on finding roots in an evolving random mother nature. Francis Crick, famous for the discovery of the double helix pattern in DNA, was such a scientist. When he failed to show the possibility of random evolution toward a primordial biological soup, he and a colleague suggested that probably some extraterrestrial aliens infested the Earth with bacteria, billions of years ago. (Ref 19) It is sad that some people have such a God-phobia that they desperately seek ways to circumvent the evidence of design which is so glaring in the study of life and the cosmos.
Perhaps the key to gaining God enlightenment is predicated on basic human humility to admit limitation. The Bible tells a story depicting human arrogance, when men desired to build the Tower of Babel to pronounce their greatness (Genesis 11). D. Knuth, a world-class scientist and top computer mathematician in the 20th century, lamented the trend of scientism. He once taught a Sunday school class based on all the 3:16 verses in the Bible, obviously inspired by the best known John 3:16. He applied some modern math to help understand the contexts of these verses and published a book titled 3:16. (Ref 20) Knuth said, “It is tragic that scientific advances have caused many people to imagine that they know it all, and that God is irrelevant or nonexistent. The fact is that everything we learn reveals more things that we don’t understand…. Reverence for God comes naturally if we are honest about how little we know.” (Ref 21)
The words of a humble scientist E. Wigner, who was awarded the Nobel Prize in 1963 for his discovery of mathematical symmetry principles as applied to subatomic particles, are worth repeating and heeding: “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.” (Ref 22) We humans should count our blessing for this miracle and gift.
(Edward W. Ng is an American Applied mathematician who has also held the positions of senior scientist, senior engineer and technical manager in the U.S. Space Program. He is noted for his broad variety of mathematical applications in space science and engineering. He has also contributed conscientiously in the spin-off of technology from the space program, with applications in such diverse subjects as Bose-Einstein distribution in mathematical physics, symbolic and algebraic computation, computational physics and biomedical research.)