Just as any language is an invention. Even the lowest of the species have language. Are they capable of invention?
The natural principles described by mathematics are pre-existing. So how come we first "invent" an area of mathematics and only subsequently "discover" that it describers Nature?
I would argue that historically this is not the order of these two events. It is only recently that a few obscure areas of mathematics have been shown to have physical "manifestations". For instance, I read recently about an example involving the Banach-Tarski paradox.