What is true is that since we have computer-based theorem provers / proof checkers, "working it out" becomes a matter of getting your challenge past one of those, and the orthodoxy will have a hard time arguing against that.

But OTOH you see many people in other disciplines challenging the orthodoxy (in Physics: string theorists, MOND proponents, etc.) and while their views aren't always taken fully serious, their houses aren't being torched either.