Is Mathematics discovered or invented?

Well, that's an interesting question. I assure you, you won't find a consensus regarding that issue. Philosophers of science, mathematicians, and physicists fall into two camps.

There are those who say it is invented. Their argument is that mathematics is just a useful tool to explain the regularity of the observable world. But some like David Hume assert that such regularity exists only in our perceptions and is not intrinsic to the outside world. They claim that the trait of observing patterns served an evolutionary role in that organisms that could make pattern out of the chaos of the physical world had a survival advantage. They further claim that for something to exist, it needs to have a casual power over the observable world, which numbers don't have. So if they don't exist, they can't be discovered for they never existed in the first place. So they're only a useful invention.

Meanwhile, there are the 'Platonisits' who claim that mathematical truths do have an objective existence. They use the 'unreasonable effectiveness of mathematics' (quoting Eugene Wigner) to describe the physical world as an evidence. Mathematicians and Physicists are often in competition. Mathematicians are usually triumphant when they come up with branches of mathematics that have no use for Physicists whatsoever. And they came up with hyper-space mathematics which at first didn't seem to have a physical application. But later on, the Physicists discovered the String Theory. And they found the hyper-space mathematics effective and indispensable to structure their theory. So every area of mathematics that is conceivable seems to have a physical application. This can only be explained if mathematics is in some way intrinsic to nature, and has an 'objective' existence of its own. We can also mention the famous Mandelbrot Set. It contains such beautiful patterns. But it is described by a single, seemingly trivial, mathematical relation. In fact, Benoit Mandelbrot, upon stumbling on this set, felt like he only discovered it, and not invent it.

So I can't give you a clear cut answer. In fact, no one can. But as for myself, I prefer 'Platonism'. I believe mathematics is discovered. You can choose your own stance.