Is mathematics something inherent to nature, or is it a purely human construct?
I believe that mathematics is not a human construct. Humans just mimic the world around them. And in our attempt to understand the mimicry we applied symbols to objects. Math is a language, just as brail is a one or sign language, it is just another way for us to transfer our understanding to one another, to transfer data.

Why do you think math is so effective in describing the physical world around us?
Because it mimics the world around us. It is copy and pasting what see, or believe to real into a language structure that allows for complex communication.

Do you think math exists by itself without physics?
Neither could exist without one another, physics is the philosophization of math, and math is the language used to transfer the philosophy of physics to one another.
If a tree falls in the woods and no one is around to hear it, does it still make a sound? If math didn’t exist, would physics still exist? Let us say that if we used another form of language another form of symbol to understand the concepts around us, the symbol doesn’t matter if it is a 1 or a 0 or a dictionary of different shaped rocks. The same principles would still arise, one rock would mean one rock and a differently shaped rock would mean two rocks. We would just ascribe it to something else. The concept was hidden within, and it was in our perception of the world that we unlocked the answers that lay before us. If math didn’t exist, then neither would physics, nothing would exist, because then there would be nothing to mimic.