Does the coloured Jones polynomial know the hyperbolic volume of a knot complement? Kashaev's 1997 guess, verified case by case, proved in none in general.
The Problems
Not schoolwork — the questions that resisted Erdős, Hilbert, and everyone since. The club keeps three shelves: what is still open, what AI recently settled, and what took humanity centuries.
Tagged knot-theory — 1 entry. Clear