I guess they mean it accurately captures the "mathematical culture" surrounding this problem, which I can confirm.
I assume that the characterisation of the problem as 'dangerous', 'alluring', tempting', etc. to mathematicians is accurate.
meh. No, I think this is the sensationalization we expect from pop-sci accounts.
I understand it as that people with expert knowledge from the field, mathematicians in this case, agree with the classification of the problem on a social and cultural level.