The Applicability of Mathematics Argument
In 1960, Nobel Prize–winning physicist Eugene Wigner published his now-classic essay “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” In it, Wigner marveled at the uncanny way abstract mathematics — often developed with no thought of application — nevertheless proves indispensable in describing and predicting the physical world. From the equations of quantum mechanics to the geometry of relativity, mathematical structures not only fit nature but frequently anticipate new discoveries. Wigner famously called this success of mathematics “a wonderful gift which we neither understand nor deserve,” and even described it as a “miracle.” Yet Wigner offered no ultimate explanation for why the universe is so deeply mathematical. His reflections raise a profound question: why should the language of human-devised mathematics map so perfectly onto the fabric of reality? For the theist, this is not a mystery at all, but rather what one would expect if the universe was created by a rational Mind who ordered it according to mathematical principles. See
The Argument
If God does not exist, the applicability of mathematics to the physical universe would be just a happy coincidence.
The applicability of mathematics to the physical universe is not just a happy coincidence.
Therefore, God exists.
Evidence for Premise 1
On naturalism, mathematics is either an abstract reality (causally inert, timeless, spaceless) or a human invention. In either case, it is deeply puzzling why these structures should map onto the physical world so effectively. As Craig puts it:
mathematics.” (Reasonable Faith)
If God exists, the universe was created by a rational mind, and it is no surprise that the world would display a rational, mathematical order.
Evidence for Premise 2
The applicability of mathematics is not trivial but profound. It not only describes known phenomena but successfully predicts unknown realities. Craig observes:
nature?” (Reasonable Faith)
The uncanny precision of mathematics in physics, from quantum mechanics to cosmology, strongly suggests that its success is not merely a coincidence.
Counter Evidence
Critics question whether the effectiveness of mathematics is really so “unreasonable.” Some argue it reflects a selection effect: we notice the mathematical models that work and ignore the ones that fail. Derek Wise, for example, writes:
Others point out that mathematical models are only approximations. Newtonian mechanics, for instance, worked within its domain but was later replaced by Einstein’s relativity. On this view, mathematics is useful, but not mysterious.
Possible Response
These objections highlight important points, but they do not undercut the argument. The selection effect explains why we keep successful models, but not why such models exist in the first place or why they so often anticipate discoveries (like the Higgs boson). Likewise, the fact that Newtonian mechanics was superseded does not remove the astonishment: Newton’s laws were still breathtakingly precise in their domain. Even approximate mathematics works with a reliability that calls for explanation. As Craig summarizes:
The theistic explanation remains stronger because it offers depth: mathematics works because the universe was designed by a rational Mind to be comprehensible.