Why does mathematics work? Think about it. Mathematical entities like numbers, sets, and equations are non-physical and abstract. They cannot 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 reflect 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 half it plays shorten a vibrating string 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. Astronomical observations later confirmed his calculations 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 person-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. The first camp includes naturalists who believe all existence is only space, time, energy, and matter. Naturalists exclude all supernatural causes. The second camp includes theistic philosophers who believe God created and design the physical universe.
Naturalists cannot provide a reasonable explanation for why mathematics applies to the physical world. It is just a happy coincidence. However, this is no explanation at all. At most, naturalists can say that it is 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. However, 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. Second, this answer still does not 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 develop according to the plan.
Mathematics and physics work well together because the same mind that designed the unive
SOURCES: Dr. William Lane Craig Videos on God and Math.