  Let $Q_n$ be the $n$-dimensional Hamming cube and $N=2^n$. We prove that the
number of maximal independent sets in $Q_n$ is asymptotically \[2n2^{N/4},\] as
was conjectured by Ilinca and the first author in connection with a question of
Duffus, Frankl and R\"odl.
  The value is a natural lower bound derived from a connection between maximal
independent sets and induced matchings. The proof that it is also an upper
bound draws on various tools, among them "stability" results for maximal
independent set counts and old and new results on isoperimetric behavior in
$Q_n$.
