I'm so used to thinking this way that I don't understand what all the fuss is about, mathematical objects being "real". Ideas are real but they're not real in the way that rocks are.
Whenever there's a mysterious pattern in nature, people have felt the need to assert that some immaterial "thing" makes it so. But this just creates another mystery: what is the relationship between the material and the immaterial realm? What governs that? (Calling one or more of the immaterial entities "God" doesn't really make it any less mysterious.)
If we add entities to our model of reality to answer questions and all it does is create more and more esoteric questions, we should take some advice from Occam's Shovel: when you're in a hole, stop digging.