The Miracle of Mathematics

Perhaps the grandest pursuit of contemporary theoretical scientists is their search for a single theory that would explain all the laws of physics in a single equation. The quest is based on the assumption that there's a rational unity to the universe, that the universe can be completely explained mathematically.

Suppose, though, that the standard explanation for the origin of the universe, that it came into being in a massive expansion of mass/energy from a single infinitely dense point, is true. If so, why should scientists, or at least naturalistic scientists, assume that a mindless eruption of mass/energy out of nothing should obey the laws of mathematics? Where does the math that describes the world come from?

A fellow at Uncommon Descent quotes several very bright people on this question.

For example, there was this from Nobel laureate Eugene Wigner who wrote in 1960 that,

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.

Wigner also wrote this:

certainly it is hard to believe that our [mathematical] reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess.

It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.

In a 1952 letter to his friend Maurice Solovine, Albert Einstein stated that the mathematical order of the cosmos and the fact that we can comprehend that order is something of a miracle:

You find it strange that I consider the comprehensibility of the world ... as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton’s theory of gravitation, for example, is wholly different.

Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the ‘miracle’ which is constantly reinforced as our knowledge expands.

There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles.”

The astonishing ability of human reason to comprehend the universe, the fact that the universe is explicable in terms of our mathematics, is very difficult to explain on any naturalistic view of the universe's origin. Why should scientists entertain the expectation and hope that they'll eventually discover a single unified theory that explains everything? Why, on naturalism, should they assume that there's an underlying rational, mathematical structure to the cosmos?

The fact that there is such a structure makes sense on a theistic worldview but is simply a leap of blind faith on any naturalistic view.

As David Klinghoffer, writing at Evolution News, once put it:

Why in the world would a scientist blithely assume that there is or is even likely to be one unifying rational form to all things, unless he assumed that there is a singular, overarching intelligence that has placed it there? Why shouldn’t the world be chaotic, utterly random, meaningless?

Why should one presume that something as orderly and rational as an equation would describe the universe’s structure?

I would argue that the only finally reasonable ground for that assumption is the belief in an intelligent Creator, who has already thought into the world the very mathematics that the patient scientist discovers.

Whatever the case, it truly is remarkable that the universe lends itself to rational inquiry by intelligent minds. Is this just an enormously improbable coincidence or is Klinghoffer correct?

Imagine that an 18th-century linguist constructed an entire language - replete with grammatical rules, a dictionary, etc. - completely in his mind. Imagine that he then learns of the discovery of tribe of people previously unknown to exist who spoke exactly that language.

Few would think that a coincidence. Rather they'd think instead that the linguist must've know about this tribe. Coincidences like that are so astronomically improbable as to cast a lot of doubt on the linguist's honesty.

The relationship of mathematics to the world is something like that. Mathematicians create mathematical systems and then it's discovered that they actually describe phenomena in the physical world.

This is why people like Einstein and Wigner think this correlation to be a "miracle."

This short video gives further explanation of the problem: