Interesting question. As long as the controversies remain in the field of abstract/theoretical mathematics, I guess it would be hard to resolve them, but I woul

Interesting question. As long as the controversies remain in the field of abstract/theoretical mathematics, I guess it would be hard to resolve them, but I would guess that if a controversial statement (not just a controversial proof) would be applied at some point to practical problems (in science or engineering) then reality would quickly point out who was right...