Updated 12-17-2020

Theologians have put forth various arguments for supernatural based on mathematics.

I have a good background in Mathematics and Physics. This post will be my own point of view.

{Terminology : When I write ‘willy nilly’ that means no patterns exist. No ‘laws of nature’ exist. Complete and utter randomness at every level. Complete chaos. The total inability to make any predictions of the world and the total inability to describe the operation of the world. Willy Nilly does not include those interpretations of Quantum Mechanics that suppose there is randomness in the world. Because, even those interpretations have precise equations describing the alleged randomness which in turn allow the predictions of ensembles, large masses and how averages behave.

When I write of mathematical models I mean the equations that physicists use and that would include chemistry. It would include so called laws of nature.}

Some math may be likened to a game. Some games (for example chess) have made up pieces and made up rules on how the game is played. In many math subjects there are made up objects, definitions and axioms and the rules of the math game. The rules may also include certain types of logic axioms. People then try to deduce what follows from all that. Those sort of math subjects are no more mystical than say chess. (Sometimes the definitions and axioms and rules are based on observations of nature and so may in fact model nature. If the math provides for certain predictions then it may turn out we find those predictions occurring in nature.).

Some math is really just tautologies. A simple example is the solution to the equation x = x/2 + 3 which gives x = 6. Those sort of math subjects are not mystical but tautologies. You may object that there is something deeper in some equations and they are not tautologies. My response is that if you were intelligent enough you would comprehend and see the tautology. Instead we have to work out the solutions and then think we have discovered something.

I think most if not all math falls into the two categories: Games and Tautologies and do not provide any evidence for supernatural anything.

Some Theologians attempt to argue for the existence of the Lord using math and physics. For example per Dr. William Lane Craig (WLC):

1. If God does not exist, the applicability of mathematics to the physical world is just a happy coincidence.

2. The applicability of mathematics to the physical world is not just a happy coincidence.

3. Therefore, God exists.

I am of the opinion that our world does not operate willy nilly. The world behaves in a way that can be modeled by math, even if we do not know what the correct math models are at the deepest level. The worlds behaves a certain way and we model it using math. This is not to advocate the world is made out of math. Also, I am not sure the objects of the math models have their correspondence in the world. For example, I am not sure something called Hilbert Space really really exists in the world even though we can model the behavior of tiny particles by assuming they have “states” in Hilbert Space and follow the mathematics of Hilbert Space.

It is my opinion the world is not being
controlled by math. Rather, the math is modeling how the world behaves.
The world happens to follow certain patterns and those patterns can be
described by math.

There are many branches and subjects in math and some have been found useful to model the world. No doubt new branches of math will be invented in the future some of which may be found to have utility to model the world. Physicists observe the world and how it behaves and have developed math tools or borrowed them from mathematicians to model the behavior of the world they have been observing. Sometimes the mathematics makes predictions which are later found out to be true. That gives additional support that the model is doing a good job modeling nature. One example is Einstein’s Special Theory of Relativity which in part was motivated to resolve the problem that Maxwell’s Equations were inconsistent with certain parts of Newtonian physics. Einstein later noticed that his model predicted the equivalence of mass and energy, the famous E=M*C*C. M being mass and C being the speed of light and E being Energy. His prediction was not confirmed until years later.

Does any of this mean G-d must have designed the world based on math or decreed that math would govern it ? I do not see a problem with the claim ‘it is a brute fact the world follows certain patterns which can be modeled by math'. Why does the world have any patterns ? That too can be a brute fact.

Was the Lord constrained to make the world in a particular way ? Could the Lord have made a willy nilly world or that operates in a way that can be modeled by one mathematical model or perhaps another etc: ? If we assume we live in a world that can be modeled by a particular mathematical model it does not follow the Lord was involved, since the Lord could have made a willy nilly world or a world modeled on a different mathematical model , right ?

Some might object that ANY world that can be modeled by math needs to have the Lord as it’s designer. I do not see how positing the Lord as a designer has any more explanatory power than just claiming ‘it is a brute fact the world follows certain patterns which can be modeled by math'. I am not sure claiming the Lord Did IT has any explanatory power at all. It is really an invocation, even a pure invention of the imagination of a big mystery thing called the Lord, that is alleged to explain what is alleged to be an issue that cries out for an explanation.

Finally, if our world was willy nilly it strongly suggests we would not have evolved or exist long enough to ask questions. The reason why we can ask questions is because we live in a region were things are not willy nilly and thus have patterns and thus sometimes can be math modeled. In other words why do we observe our region has patterns and can be modeled by math ? Because if our region was willy nilly then it would not have patterns (and therefore could not be modeled by math) and thus we would not be here. But since we are here that means our region has to have patterns and thus be susceptible to being modeled by math.