Physicist: This question usually comes in the form of “are complex numbers real?” or “are negative numbers real?” or something along those lines. If you think of “realness” in terms of what can be touched, or observed, or measured, then numbers (all kinds of numbers) are clearly not real. Regular numbers are great at describing some things (like how many turtles are around), but there are a lot of patterns in nature that can’t be so easily described and require different kinds of “mathematical objects”, like negative numbers, non-integer numbers, complex numbers, matrices, polynomials, lots of stuff. The quantum mechanical wave function of a turtle (or anything else) is described using complex numbers, because trying to do quantum mechanics without complex numbers is practically impossible. About as hard as counting turtles without the (obviously “real”) natural numbers.

When you want to outsmart the world, you turn to the facts. And the facts are in the science.