"The only reason mathematics is admirably suited describing the physical world is that we invented it to do just that. It is the product of the human mind and we make mathematics up as we go along to suit our purposes. If the Universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess, or any other set of rules with relational structures that we contrived. Mathematics is not discovered, it is invented. This is the non-Platonist position.
... The non-Platonist view is that, first, all mathematical models are approximations of reality. Second, our models fail, they go through a process of revision, and we invent new mathematics as needed. Analytical mathematical expressions are a product of the human mind, tailored for the mind. Because of our limited brainpower we seek out compact elegant mathematical descriptions to make predictions. Those predictions are not guaranteed to be correct, and experimental verification is always required. What we have witnessed over the past few decades, as transistor sizes have shrunk, is that nice compact mathematical expressions for ultra small transistors are not possible. We could use highly cumbersome equations, but that isn’t the point of mathematics. So we resort to computer simulations using empirical models. And this is how much of cutting edge engineering is done these days.
... I believe a non-Platonist position gives us greater freedom of thought. If we accept that mathematics is invented, rather than discovered, we can be more daring, ask deeper questions, and be motivated to create further change." - Derek Abbott