Why do mathematics explain the physical world so well? Is it just a happy co-incidence or is there an intelligent mind behind it?
Why does mathematics work? Think about it. Mathematical entities like numbers, sets, and equations are non-physical and abstract. They can’t cause anything, yet for some reason, the physical universe operates mathematically. As Galileo put it, “The book of nature is written in the language of mathematics.” “Scientists do not use mathematics merely as a convenient way of organizing the data; they believe that mathematical relationships reflects real aspects of the physical world.
Science relies on the assumption that we live in an ordered universe that is subject to precise mathematical laws. Thus the laws of physics are all expressed as mathematical equations.” For example, Pythagoras discovered that when a vibrating string is shortened by half, it plays the same note one octave higher. Isaac Newton’s observations led to his discovery of the law of gravity, a mathematical relationship expressed as a simple equation that enabled us to enter the Space Age. Mathematics enabled astronomers to pinpoint the location of a previously undiscovered planet, and James Clerk Maxwell used mathematics to predict the existence of radio waves. Albert Einstein, working with theoretical mathematics developed fifty years earlier, formulated his general theory of relativity, a pillar of modern physics. His calculations were later confirmed during the solar eclipse when Arthur Eddington observed light from distant stars bending around The Sun. Then, Peter Higgs used mathematical equations to predict the existence of an elementary particle. It took 48 years, billions of dollars, and millions of man-hours for experimental scientists to finally detect the Higgs boson. How do we explain the astonishing applicability of math to the physical world?
In 1960, the Nobel prize-winning physicist and mathematician, Eugene Wigner, published an article that stunned the scientific community entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Wigner concluded that the effectiveness of mathematics is a “miracle… which we neither understand nor deserve.”
Why is mathematics so effective? Philosophers who address this question fall into two camps: naturalists, who believe that all that exists concretely is space-time and its physical contents – they exclude supernatural causes – and theists, who believe in a God who created the universe. Naturalists cannot provide a reasonable explanation for why mathematics applies to the physical world. It’s just a happy coincidence. But this is no explanation at all. At most, naturalists can say that it’s not surprising that math applies to the world because the world itself just happens to have a mathematical structure, so of course mathematics applies to it. But this explanation is unsatisfactory for two reasons. First, a great deal of mathematics in science cannot be physically realized, for example imaginary numbers and infinite dimensional spaces. Although these concepts are useful, physical reality cannot possibly have the structure they describe. And second, this answer still doesn’t explain why the physical universe has such a stunningly elegant mathematical structure.
By contrast, for theists, mathematics works so well in the physical world because God has chosen to create the world according to the plan he had in mind. The first century Jewish philosopher Philo of Alexandria offered this analogy. When a king wants to build a city, a trained architect first designs in his mind a plan of all the parts of the city that are to be completed. Then he begins to construct the city out of stones and timber, looking at the model and ensuring that the material objects are built according to the plan. Mathematics and physics work so well together because the same mind that designed the universe on a mathematical model also built the universe on the same mathematical model. All of this adds up to an argument for the existence of God that goes like this. If God does not exist, the applicability of mathematics is just a happy coincidence. But the applicability of mathematics is not just a happy coincidence. Therefore, God exists. Eugene Wigner was right; the effectiveness of mathematics in the physical world is quite literally a miracle, which is best explained by the existence of God.