Why did the natural world always – so far as we know – obey laws of mathematics?

As argued by scholars such as Philip Davis and Reuben Hersh, mathematics exists independent of physical reality. It is the job of mathematicians to discover the realities of this separate world of mathematical laws and concepts. Physicists then put the mathematics to use according to the rules of prediction and confirmed observation of the scientific method.

But modern mathematics generally is formulated before any natural observations are made, and many mathematical laws today have no known existing physical analogues.

Einstein’s 1915 general theory of relativity, for example, was based on theoretical mathematics developed 50 years earlier by the great German mathematician Bernhard Riemann that did not have any known practical applications at the time of its intellectual creation.

In some cases the physicist also discovers the mathematics. Isaac Newton was considered among the greatest mathematicians as well as physicists of the 17th century. Other physicists sought his help in finding a mathematics that would predict the workings of the solar system. He found it in the mathematical law of gravity, based in part on his discovery of calculus.

At the time, however, many people initially resisted Newton’s conclusions because they seemed to be “occult.” How could two distant objects in the solar system be drawn toward one another, acting according to a precise mathematical law? Indeed, Newton made strenuous efforts over his lifetime to find a natural explanation, but in the end he could say only that it is the will of God.

Despite the many other enormous advances of modern physics, little has changed in this regard. As Wigner wrote, “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”

In other words, as I argue in my book, it takes the existence of some kind of a god to make the mathematical underpinnings of the universe comprehensible.