- Nobody knows the geometric shape of a tight trefoil knot.
I asked around. It is true. Even a school child knows the shape of a tight torus. But nobody knows the shape of a tight granny knot. Nobody. Nor that of any other knot. Open or closed, it makes no difference: the shapes are unknown.
Take a rope, add a knot, pull it tight. Ask your mathematician friend to describe the shape. He cannot! What, he can solve Fermat's theorem but cannot solve this little problem? And he is still working on the Riemann conjecture? Tell him to do something sensible instead, like this little problem! He will become famous on his own right. And he will help the proof of the theory of everything.