If you develop a mathematical proof, then you will have proven something.
If you develop a scientific theory using math, then you will have created a model that is subject to forecasts and testing.
In science, however, you don't ever prove anything. You only ever accumulate additional evidence of its veracity / disprove it when evidence shows it to be flawed.
Nothing is ever certain in science. Nothing is ever proven (though, for many circumstances, for simplicity we generally assume it is given overwhelming weight and consistency in the evidence).
So what does that mean for any equation I develop to support the principles of my theory? Does it mean the equation is always in doubt (stands to be corrected)
Let's say my theory has a hole in it or is missing some unknown component, there is an equation that fits regardless?
Encourage you to explore this same phenomenon when looking at gravity from a Newtonian perspective versus an Einsteinian one. Both are correct, given specific circumstances, and the math is extremely powerful and helpful, but clearly have holes in other circumstances (quantum level, for example).
If an equation can be developed for any good theory then does it only imply the theory is correct?
Having an equation is often necessary, but never sufficient.