Somewhat surprisingly , given their wide range of practical uses , it has not yet been proven that in three dimensions solutions always exist ( existence ) , or that if they do exist , then they do not contain any singularity ( they are smooth ) .
Somewhat surprisingly , given their wide range of practical uses , mathematicians have not yet proven that in three dimensions solutions always exist ( existence ) , or that if they do exist , then they do not contain any singularity ( or infinity or [ discontinuity ] ) ( smoothness ) .