There are two tenable but diametrically opposed paradigms for understanding the correspondence between mathematics and physics, a dichotomy that arguably goes as far back as Plato and Aristotle. According to the Aristotelian paradigm, physical reality is fundamental and mathematical language is merely a useful approximation. According to the Platonic paradigm, the mathematical structure is the true reality and observers perceive it imperfectly. In other words, the two paradigms disagree on which is more basic, the frog perspective of the observer or the bird perspective of the physical laws. The Aristotelian paradigm prefers the frog perspective, whereas the Platonic paradigm prefers the bird perspective.
As children, long before we had even heard of mathematics, we were all indoctrinated with the Aristotelian paradigm. The Platonic view is an acquired taste. Modern theoretical physicists tend to be Platonists, suspecting that mathematics describes the universe so well because the universe is inherently mathematical. Then all of physics is ultimately a mathematics problem: a mathematician with unlimited intelligence and resources could in principle compute the frog perspective--that is, compute what self-aware observers the universe contains, what they perceive, and what languages they invent to describe their perceptions to one another.
