Do the old words stop describing old things once we invent new words to describe new things? However, very accurate measurements of the precession of the planet Mercury necessitated an overhaul of Newton's theory of gravity in the form of Einstein's general relativity.
The whole "math is invented vs discovered" argument is centuries old and it it's far from binary. Many prominent mathematicians and physicists (Einstein, Hilbert and Cantor, to name a few) thought that math an invented set of tools and it seems that most practitioners hold similar beliefs. The reality is that mathematics is probably both invented and discovered, in a very weird way. First, we invent mathematical concepts by way of abstracting elements from the world around us. We come up with conceptualizations about shapes, lines, sets, groups, and so forth, either for some specific purpose or simply for fun. They then go on to discover the connections among those concepts. This iteration of invention and discovery is man-made, so our mathematical concepts are ultimately based on our perceptions and the mental pictures we can conjure. One would imagine, for example, should we live in a perfectly continuous world would not have invented natural numbers early on but instead relied on some sort of continuous mathematics for daily use.
When a tennis ball machine shoots out balls, you can use the natural numbers 1, 2, 3, and so on, to describe the flux of balls. When firefighters use a hose, however, they must invoke other concepts, such as volume or weight, to render a meaningful description of the stream. So, too, when distinct subatomic particles collide in a particle accelerator, physicists turn to measures such as energy and momentum and not to the end number of particles, which would reveal only partial information about how the original particles collided because additional particles can be created in the process.
It's evolutionary, too - over time only the best models survive. Failed models, (like Descartes vortices of cosmic matter) die in their infancy or get disproven later. In contrast, successful models evolve as new information becomes available and stick around - the area of a circle is as true today as it was two centuries before.
Whats incredible is that mathematicians sometimes develop entire fields of study with no practical application in mind, and yet decades, even centuries, later physicists discover that these very branches make sense of their observations. Galois, for example, developed group theory in the early 1800s for the sole purpose of determining the solvability of polynomial equations. The general idea is that groups are algebraic structures made up of sets of objects (say, the integers) united under some operation (for instance, addition) that obey specific rules (among them the existence of an identity element such as 0, which, when added to any integer, gives back that same integer). In 20th-century physics, this rather abstract field turned out to be the most fruitful way of categorizing elementary particles. There are plenty of other examples like that, topology and number theory to name the few.
Anyway, while it's fun to discuss mathematics and it's origins, I can't imagine someone believing or not believing in God because of the effectiveness of mathematics. What belief really boils down to is an emotional choice which is made relatively early on in life. Every argument is usually a justification of that choice. Some people are distrustful of anything they have not seen and they turn out like me. Some people turn out like you. This said, if being religious makes you more likely to make ethical choices, I am all for you being religious.
