In mathematics, the Seifert conjecture states that every nonsingular, continuous vector field on the 3-sphere has a closed orbit.
In a 1950 paper, Seifert asked if such a vector field exists, but did not phrase non-existence as a conjecture.
The existence of smoother counterexamples remained an open question until 1993 when Krystyna Kuperberg constructed a very different
Later this construction was shown to have real analytic and piecewise linear versions.
possess closed flowlines[1] based on similar results for Beltrami flows on the Weinstein conjecture.