> Which we hear a lot these days but which is extremely difficult to prove.

I would say that is extremely easy to prove but writing a solid paper on that consumes a lot of resources. That is why conjectures are part of the scientific method: we can discuss about things that we think are true or not before making a multi-year effort to prove the point in a scientific way.

The problem is when people confuse scientific publications with truth. In math that would be easier for the practitioners but in social sciences we know that we can publish ala Sokal affair.