God, mathematics, and randomness

Several writers have dwelled on the “unreasonable suitability” of mathematics to describe the workings of the Universe. Others have speculated on the ontological status of mathematics: is it “manmade”, or was “created” by God and has an independent “Platonic” existence. These topics have been covered by numerous writers in great detail so I don’t want to repeat them here.

For me the question is not so much whether mathematics was created by God but whether God (and infinite being) can solve all the heretofore unsolved problems and those that have been proven to be unsolvable.

Let me start with the simplest illustration. The value of π can not be expressed by a finite number of digits. Does God know all of them? If so, how does He do it? Even if God is infinite and eternal, π too is infinite.

A second, related question concerns the Goldbach Conjecture, that every even number can be expressed as a sum of two primes. So far this has not been proven and it may be that true that it is unprovable. Assuming that there is no proof, would God know whether the conjecture is true or false. To do so, He would have to go through an infinity of numbers which must be hard even for an infinite being.

Another problem that hounds me is randomness. I do not understand the master of randomness, Gregory Chaitin. But it is clear to me that even though the digits of π are random, they are not completely random because another being on another planet can arrive at the same number at, say, the 200th digit. Chaitin has come up with his famous Ω which sounds as random as they come. Except that apparently he and others have come up with even “higher order” of randomness. Can God predict the digits that these randomness formulas define? The way I see it, if the definition is in a closed form, then an infinite being should be able to see whether it is or not. But I don’t know enough about this topic.

But, quantum events are random. While we can predict average properties and events, we can never predict individual quantum events. Can God do it? If He can then these events are not truly random, and Einstein would be correct in that there are “hidden variables”, something the Bell inequality has disproved seemingly conclusively. If He cannot, then He must have difficulty knowing everything about the Universe: how could He if He cannot even predict the decay of an atom? But things look bad for Him even if somehow He could predict or observe: no sooner would He observe an individual subatomic orthogonal property (position and momentum or time and energy) the corresponding property would be unknowable even by Him. Or else Quantum Theory is incorrect or at least incomplete.