I agree with that, but I wasn't clear I think. You can find euclidian geometric proof of some standard arithmetic theorems, but geometry isn't the right tool t

I agree with that, but I wasn't clear I think. You can find euclidian geometric proof of some standard arithmetic theorems, but geometry isn't the right tool to prove really complex arithmetic theorems. Try to make euclidian geometry complete enough to resolve all arithmetic, and you will probably find yourself in front of contradictions (I stopped doing math after my bachelor, so I clearly might be wrong about that). Why do we need to expand th9se theory? First correct the issues left within the defined context. Then find more contexts and see if you can define a new theory or use an old one?