A problem of Ulam about magnetic fields generated by knotted wires
  In the context of magnetic fields generated by wires, we study the connection between the topology of the wire and the topology of the magnetic lines. We show that a generic knotted wire has a magnetic line of the same knot type, but that given any pair of knots there is a wire isotopic to the first knot having a magnetic line isotopic to the second. These questions can be traced back to Ulam in 1935. 
Alberto Enciso and Daniel Peralta-Salas
math.DS math-ph math.CA math.MP