A Milnor fiber of an isolated hypersurface singularity 
is the nearby smooth level 
for sufficiently small
nonzero 
relative to a small ball radius 
. Its homotopy type
is a bouquet of spheres of real dimension 
, with their number equal to the Milnor
number. Thus the Milnor number measures the
middle-dimensional topology of this smoothing.
An ordinary quadratic singularity has one such sphere. The mu-constant problem concerns continuous trivialization of the entire ambient family and its defining functions, a stronger statement than equality of these individual fiber invariants.
