I believe there is something permanent, even eternal, about mathematics–even if they can’t make a rigorous mathematical argument to justify their intuition. Maybe this doesn’t seem surprising if you've heard someone say it before, but I think it is surprising. After all, math is just an abstraction, something imagined and defined by humans; there’s no reason a priori we should expect to describe the universe, let alone touch a truth which is deeper than the universe–or is there?
Math is the application of logic to notions of quantity.
If we assume A and B about numbers and we apply reason, C and D necessarily follow. Since math is a type of logic, if logic is eternal and immutable, we should expect math to be. If logic underlies the physical structure of the universe and the interactions between various particles and wave forms, then we should expect mathetmatics to aptly describe the universe. All we need to do is invent a mathematical object with similar enough structure to a certain physical object, and we have a useful mathematical model of it.
So is logic actually fundamental to the way things work?
Is logic a universal truth that lies behind and constrains everything in the universe? In quantum mechanics, there seem to be events we can’t predict–probabilistic events. Scientists question the notion that events are inexorably determined by physical laws; some events are predictable, others are random. We are no longer at the mercy of Fate; we are at the mercy of both Fate and Chance. Quantum mechanics quashed long-held ideas about logic directing the universe. But even quantum probabilities can be described by mathematics. Maybe logic wins after all.
I have faith that logic is real and fundamental to everything that happens. This is not blind faith because it is supported by empirical evidence. I see people using reason every day to understand events around them and their efforts paying off. But it still takes faith to believe in logic. If I wanted to prove that logic works,
I would have to use logic to prove it–that would be circular reasoning!
By faith, therefore, mathematicians understand that even if the specific system of axioms they use is arbitrary, their conclusions drawn from those axioms by logic touch on something fundamental to the nature of reality. To me math seems very similar to theology. Both grasp at the infinite, the eternal, the fundamental; both are caught up by their beauty; both confess by faith that their influence permeates the physical universe, but extends beyond it.