Since the emergence of the Enlightenment atheism and the idolization of scientific method as the “true path to knowledge,” Christian apologists have been pointing to an obvious problem: Neither human reasoning nor human observation can explain the world. The human brain can only discover new things within a framework of a priori presuppositions; these presuppositions must by necessity come by either intuition or revelation. There must be a God or gods somewhere in the equation, otherwise scientists are only discovering but not explaining. The atheist Laplace, when challenged by Napoleon Bonaparte about the absence of any mention of the Creator in his Exposition of the System of the World, replied dryly, “I had no need of that hypothesis.” When Napoleon told another great mathematician and scientist, Joseph-Louis Lagrange, about Laplace’s reply, Lagrange exclaimed, “Ah, but it’s a fine hypothesis, it explains so many things!”
In the century after Laplace, atheist scientists gradually realized how right Lagrange was. In fact, more than just “explaining many things,” the “God hypothesis” turned out to be irreplaceable when it came to explaining the world. Science kept discovering but it could explain less and less. Worse than that, science couldn’t explain its own existence. Why do we as humans know what we know, and why do we discover what we discover, why do we understand what we discover, and why is everything we discover so beautifully fitted to serve man’s needs? The atheism of the Enlightenment had proposed that the more science discovers, the more it will explain about man and his nature, and therefore the less need for theology or religion. “A hundred years after my death,” boasted Voltaire, “the Bible will disappear from the face of the earth.” But by the 1950s even atheist scientists were having doubts as to the ability of science to explain anything, no matter how much it discovered, and no matter how many forces of nature it was able to harness to serve man and his civilization.
And then, the decisive blow came, and it came not from a theologian or a Christian apologist, it came from a respectable scientist who three years later would receive the Nobel Prize for his contributions to physics: Eugene Wigner. In his 1960 article, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” Wigner stated the truth which every atheist scientist and philosopher knew and was afraid to tackle: Mathematics and physics, originating from two completely different quarters, the former from the pure speculations of the mind, the latter from the empirical data the physical reality feeds our experience with, have no reason to be connected in any comprehensible or predictable way. And yet, mathematics has been wonderfully effective in describing physical laws and predicting outcomes of experiments in the real world. Why, asked Wigner, and couldn’t find an answer. No one can. Scientists keep using math and relying on math, as if they know for sure that math must be relevant to our physical experience. But they can’t explain why. The arrogant claim that science will explain the world more and more came to an end; science can’t even explain itself anymore.
Wigner added insult to injury when he ended his article using almost religious language of humbleness, gratitude and faith:
Let me end on a more cheerful note. 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.
Miracle. Wonderful gift. We neither understand nor deserve. We should be grateful. We should hope. Wigner, the mathematician and scientist, sounded like the Lutheran pastor in the church where his parents – converts from Judaism – took him when he was a boy. He was a stroke of a pen away from placing all mathematics and physics at the feet of the Creator and admit that without Him, nothing could be explained; and only the existence of God could account for the mysterious connections between the speculations of our brain (mathematics) and the laws of the real world.
In short, Wigner committed a treason against science. He didn’t, in an Einsteinian fashion, just declare a personal faith in a God that had only marginal relevance to his scientific studies. He went farther than that: he implied that science was impossible and inexplicable without accepting a higher reality, transcending the mind of man and its capabilities for reasoning and experimentation. The short and ostensibly innocent article faced some really violent reactions; some objected to the conclusions in it, others to the premises, and still others refused to even deal with it, pretending it had never been written. But Wigner remained right about one thing: Despite the many attempts, no one could give a rational explanation for what Wigner described as the “uncanny ability of mathematics to describe and predict accurately the physical world.”
In 2009 the Romanian-Israeli-American astrophysicist and mathematician Mario Livio took up the task to write a book with the purpose of neutralizing the conclusions of Wigner’s essay for the popular reader. Livio apparently understood very well what the conclusion of Wigner’s article is, for he titled his book, Is God a Mathematician? A deceptive title, to start with. Livio has no intention of discussing God or His relation to science. The title is only an admission that the impossibility to explain the connection between mathematics and physics leads to only one place – the God of the Bible. But the admission is only a mockery. Mario Livio has no use for God, whether He explains many things or not. He is heavily biased, and he doesn’t hesitate to flaunt his bias throughout the book. In the very first chapter, when discussing the issues about mathematics, invented or discovered, Livio asks the question: “Was God invented or discovered?” Or even more “provocatively,” in his own words, “Did God create humans in His own image, or did humans invent God in their own image?” Of course, the very question reveals that Livio doesn’t believe God created humans; the possibility that humans invented God is so illogical that a non-biased intelligent person wouldn’t even mention it. After all, how is it that generations of Christians of different cultures and geographical places continue “inventing” the same God over and over again? And why invent a God in the first place; what is the practical significance of this self-conscious self-deceit of billions of people throughout history? And what about atheists who don’t invent any God at all? Are they imageless, faceless beings, or are they so desperately incompetent that they can’t even invent? Later in the book Livio ends the chapter on Galileo with the following pompous words:
. . . at a time when there are attempts to introduce biblical creationism as an alternative “scientific” theory . . . , it is good to remember that Galileo already fought this battle almost four hundred years ago—and won!
It doesn’t take a history expert to know that the “battle” Livio talks about wasn’t about to start for another three centuries, and that Galileo controversy was all within the framework of biblical creationism; it was not a battle of cosmologies but of interpretations within the same Biblical cosmology. After Galileo, Newton and Kepler followed his lead, and both men were convinced Biblical creationists, and neither of them noticed any “victory” for atheism in Galileo’s or in their own discoveries. The fact that Livio even wrote that in a book shows that the audience he is targeting is quite ignorant of history; and it also reveals his bias, against the facts of history and of science.
With that bias, Livio sets out to solve the problem postulated by Wigner. Or, as he says, he “attempts to tackle many of these intriguing questions.” For example, is mathematics discovered or invented? Are there transcendental ideal forms, or is it all an invention of the chaotically moving human mind? The reader is left with the impression that at the end he will at least have some clarification as to what the solution to the dilemma is. As we will see, only disappointment lies ahead.
Livio traces the history of the philosophical ideas concerning mathematics. He is a master storyteller, and he can revolve a story around his main topic, illuminating the most important moments and details. Plato and Aristotle, Archimedes, Galileo, Newton, Descartes, Gaus, all come to play in helping Livio resolve the problem – or at least lead him to some “clarification.” A student of history of science will learn many interesting trivia from the book’s narrative. If nothing else, the author’s mastery in telling the story of math is unsurpassed. With a raconteur of that magnitude, by the last chapter the reader’s mouth is drooling in expectation for the solution to the double dilemma: (1) is math discovered or invented; and more important, (2) why is mathematics – a product of the human mind – so mysteriously helpful in describing physical events outside of the human mind?
The last chapter is a disappointment.
The first dilemma is resolved through low-class dialectical evasion: Mathematics is both discovery and invention. Some of it is invention, like the prime numbers. Some of it is discovery, like the theorems about the prime numbers. Livio doesn’t explain how he reconciles both. Didn’t prime numbers exist even before they were “invented”? And how do we “discover” anything about something that isn’t more than a just mental speculation? Can we “discover” theorems and laws in a book of fiction, let alone expect them to have any application and practical significance in the real world? Isn’t the “discovery” only a part of our invention itself? How can Livio be sure that the “discovery” of the theorems about prime numbers is not another figment of our imagination, just as the prime numbers themselves? Livio’s solution is not a solution at all.
When he gets to the Wigner’s Enigma, Livio is even more disappointing. He quotes irrelevant passages from other authors, and then he gets to the solutions offered to the Enigma by the computer scientist Richard Hamming, most of which rely on the evolution of humans – we just couldn’t survive as a species, y’know, if our brain didn’t evolve with understanding of calculus, vector analysis, or non-Euclidean geometries. Livio is smart enough to know that such arguments won’t fly: He quotes Hamming who is not convinced even by himself. And there are no other solutions, only conjectures.
So, if not Hamming’s solutions, then what? And here, at the end of 250 pages of struggling to find a solution, the poverty of Livio’s philosophy manifests itself. He admits there is no solution. He says there is no guarantee that mathematical theory should exist at all. He says there doesn’t have to be a theory of gravity, or a theory of anything at all! If there are any theories, it is because “nature has been kind to us all,” but we can’t even declare with any kind of certainty whether we should try to have any theories or postulate any laws of nature. Livio started from an atheistic point of departure; the goal was to explain an enigma that has baffled atheist science for decades. His journey ended in agnosticism, confusion, and denial.
To soften the effects of the disgraceful end of his philosophical quest, Mario Livio summons the spirit of Bertrand Russell to justify the failure:
Philosophy is to be studied not for the sake of any definite answers to its questions, since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves . . . but above all because, through the greatness of the universe which philosophy contemplates, the mind is also rendered great, and becomes capable of that union with the universe which constitutes its highest good.
Here is the sum of the atheist philosophy: We started strong and confident that through science we will answer all the questions and therefore won’t need God anymore; and we ended up having no knowledge and no assurance of any kind of knowledge at all, with a naked and poor philosophy that has no answers at all; but at least we feel “great” in our minds because we have asked the questions, and of course, because unlike those Christians who superstitiously seek union with their Christ, we now have our own enlightened union with the “universe” which constitutes our “greatest good.”
After finishing Is God a Mathematician? the intelligent reader will wonder, how in the world can a scientist and mathematician of Livio’s rank rest satisfied with such a meager result from his quest? Isn’t he supposed to look for answers? Do we pay scientists to settle for an unknown and unknowable universe in which nothing could be known and the questions will never get answers? How does Livio reconcile his reputation and position of a learned man with his surrender before the unknown?
The answer must be found in the fact that Livio doesn’t want an answer. He knows there is an answer to Wigner’s enigma, as well as to all other metaphysical problems of science and knowledge. The answer is simple, and by the principle of the Occam’s Razor must be accepted as operative by the scientists, if they were unbiased. The answer is that there is a Creator God, Who has created both the human mind and the world. The connection between math and physics is there, in God the transcendental originator of all, of our thinking and reasoning, and of our environment. God is not “invented” nor “discovered,” He has revealed Himself, and only through that revelation of God we know anything about ourselves, or about the world. Mathematics is indeed both invented and discovered but not in the primitive dialectical sense Livio wants it; it exists in ideal form in the mind of God, and we “discover” it through a process of divine revelation, as part of the larger revelation from God about Himself, us, and our world. Wigner was right we should be grateful for mathematics – because it indeed is a gift from God, a tool given to us to use for His glory. Contrary to Livio’s wishful thinking, biblical creationism is not defeated, it is victorious, and Livio’s atheism is an abject failure, as his own book demonstrates. Livio’s book is a failure itself, and its only value is to serve as a didactic tool to show the poverty of the atheist philosophy and science to explain anything, including its own existence and usefulness.
God is not mocked.