  The Milnor fibre of any isolated hypersurface singularity contains many exact
Lagrangian spheres: the vanishing cycles associated to a Morsification of the
singularity. Moreover, for simple singularities, it is known that the only
possible exact Lagrangians are spheres. We construct exact Lagrangian tori in
the Milnor fibres of all non-simple singularities of real dimension four. This
gives examples of Milnor fibres whose Fukaya categories are not generated by
vanishing cycles. Also, this allows progress towards mirror symmetry for
unimodal singularities, which are one level of complexity up from the simple
ones.
