Do you think that one day, we will understand mathematics so well that we won't need to work on it anymore? Can we ever explore all of it, until there's nothing left of it to find and understand?
Nope. Simply put, we cannot fathom the amount of mathematical... what's the word... I'll just say math. It would be impossible to stop advancing in math, especially to stop working on it. Mathematical applications are all over, everywhere you look, there may even be some which humanity has not discovered yet. I had a debate with my Calculus teacher about this, he told me something that kind of blew my mind, "Just as math can go to infinity, so can mankind."