Is $\varliminf_{n \rightarrow +\infty} |n \sin n| = 0$ correct, where $n$ is an integer?

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 $0$.

• That's equivalent to asking whether $n\pi$ comes within $o(1/n)$ of an integer, which is a well-known open problem; it's expected to be true (if $\pi$ is replaced by a random number then it's true with probability $1$) but well beyond what can be proved by known methods. (The Dirichlet result you quote gives $O(1/n)$ in place of the desired $o(1/n)$.) – Noam D. Elkies Oct 6 '13 at 5:55
• This question appears to be off-topic because it is about a well-known open question. – Gerry Myerson Oct 6 '13 at 6:41
• math.niu.edu/~rusin/known-math/99/dense_sine – Terry Tao Oct 6 '13 at 15:17
• This question was closed because it asks about a well-known open question. Why has it been reopened? Has someone solved it? – Gerry Myerson Nov 10 '13 at 4:35
• – Per Alexandersson Apr 22 '14 at 20:42