Let's take a look at the typical crank/non-expert 'idea'.
There is no mathematical rigour to it, indeed, there's generally no math at all. It's usually word salad, with terms being used in ideosynchratic, non-standard ways. It's almost always challenging a hundred years of experimentation and research with no experiments or derivations to support the extravagent claims. It's not that they're reluctant to accept new ideas, it's that they're reluctant to wade through reams of garbage clogging their e-mail inboxes.