TITLE: Is $\varliminf_{n \rightarrow +\infty} |n \sin n| = 0$ correct, where $n$ is an integer?
QUESTION [13 upvotes]: Is it true that $\varliminf_{n \rightarrow +\infty} |n \sin n| = 0$, where $n$
runs over the integers?
The existence of the limes inferior follows from Dirichlet's approximation theorem,
but the problem is to prove that it is $0$.

REPLY [7 votes]: This is an open question. See the comments for more details.