  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.
