You've pulled that out of thin air, so I can dismiss it in the same spirit.
No, there is no such requirement. Deal.
No, there is no such requirement. Deal.
It is the accepted way to use each other's works in the scientific community. That is why citations/references/bibliographies exist.
There's never been such a consideration that one should not work on a problem that someone else is working on or has worked on. Nor do I think it's something that should be true. Mathematics exists and is supported to benefit society, not to pamper mathematicians.
That is not what i meant at all. This is your erroneous take.
In any scientific community when people work on the same problems, if they are aware of the others work, they usually cooperate/share their findings especially if the problem is a long-standing nobel-prize/fields-medal worthy one. If one builds their approach based on others then there definitely is a citation/reference acknowledging others contributions.
This is the ethical accepted practice since the dawn of the scientific age because "standing on the shoulders of giants" and building from there is how science advances.