The way I see it, most mathematics have been developed through observances in nature to describe them. We use it as a system to make sense of the physical world ie. counting, rates of change, shapes. While the system of mathematics we currently use to describe nature has been designed and develop by humans, it still shows patterns that continue to repeat themselves in mathematics and in nature. The best examples of this are irrational values such as π and e. These are both values that consistently show up in nature, with set values that do not change. The existence of these values leads me to believe that mathematics is something inherent to nature.
Math is so effective for describing the physical world around because it can account for any observances made in the physical world through functions and equations. In physics, each physical phenomena has its mathematical counterpart that is described using either a constant, an equation, a function or a vector. Its ability to account for observances and changes makes it a powerful way to describe reality,
I believe math itself can still exist itself without physics. While both fields have mutually developed through discoveries in the other, physics will always be a form of applied math; there are still many applications outside of a field of physics. I imagine its applications in statistics, biology, chemistry, economics, medicine, programming and art as being developed independent of physics. While most can be related to physics, others can still be disconnected to it, allowing for mathematics to exist, develop and be applied while not needing physics.