Math is invented.
According to Goedel you never have all the tools necessary to prove all theorems within the current framework of theories. So you make up new ones which you mold in such a way that they help to solve your problem (or you invent the tools necessary). This means you invent solutions to your problems which then have implications that are left to be discovered. But since all the math would equally work e.g. if we chose to have not 10 but 5 as basis to build our number system which makes it arbitrary or not discoverable (the mount everest could be discovered since it is a specific mountain. A car is invented b/c there are arbitrary solutions to the problem motorized individual transport).