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.