> we have created operations

It seems that addition (for instance) was "created" long before us.

On the other hand, it seems highly unlikely that a civilization similar to ours could "invent" an essentially different kind of mathematics (or physics, etc.)

Well, I was thinking more along the lines of, say, multiplication and division - you can handle every single equation humanity has ever come up with without either of them. It might be messy and awful and annoying, but I would say in particular these operations are invented more than discovered.

So, more properly phrased, we created some operations.