Depending on how philosophical you want to get, it is not so clear what exists and what does not. Neither it is absolutely clear what means to be discovered.

I think that ideas can be discovered. In my opinion, theorems, or more precisely the proof of these theorems, for instance, are discovered. In the sense that they are not an invention, they "emerge" from more fundamental definitions.

You seem to be of the opinion that the only things that can be discovered are those that emerge from the "real world", whatever the real world is. That is, I guess, an acceptable interpretation, but I do not think is the only possibility.

To give a very concrete example, chess rules do not exist in the real world, but knight's tours are discovered.