For me, both questions "is math real" and "is math discovered or invented" miss the point. Math is a model of the universe in the same sense that a world map is a model of the earth.
Is a map real? Well, it is. I can see it on my desk. Is the earth real? It is too, but they are not the same. In that sense map is also not "real".
Is the map discovered? Well, it uses data that was mostly discovered, but some parts were "invented" or edited for simplification for the map to be useful.
The real question should be "is math useful" as a model. We all know most basic parts are, but some mathematicians forget that they are dealing with an imperfect model and keep finding paradoxes. It's like we would forget the imperfections caused by the mercator projection and be surprised the real world distances are not proportional to map distances.
That's the reason I always liked engineering more than maths. When programming you always "import" the libraries you need and find useful for the task. You only make sure that they are compatible with each other. Mathematicians "import" all axioms, call them maths, and are surprised they get paradoxes.
Is a map real? Well, it is. I can see it on my desk. Is the earth real? It is too, but they are not the same. In that sense map is also not "real".
Is the map discovered? Well, it uses data that was mostly discovered, but some parts were "invented" or edited for simplification for the map to be useful.
The real question should be "is math useful" as a model. We all know most basic parts are, but some mathematicians forget that they are dealing with an imperfect model and keep finding paradoxes. It's like we would forget the imperfections caused by the mercator projection and be surprised the real world distances are not proportional to map distances.
That's the reason I always liked engineering more than maths. When programming you always "import" the libraries you need and find useful for the task. You only make sure that they are compatible with each other. Mathematicians "import" all axioms, call them maths, and are surprised they get paradoxes.