  Cameron and Erd\H{o}s asked whether the number of \emph{maximal} sum-free
sets in $\{1, \dots , n\}$ is much smaller than the number of sum-free sets. In
the same paper they gave a lower bound of $2^{\lfloor n/4 \rfloor }$ for the
number of maximal sum-free sets. Here, we prove the following: For each $1\leq
i \leq 4$, there is a constant $C_i$ such that, given any $n\equiv i \mod 4$,
$\{1, \dots , n\}$ contains $(C_i+o(1)) 2^{n/4}$ maximal sum-free sets. Our
proof makes use of container and removal lemmas of Green, a structural result
of Deshouillers, Freiman, S\'os and Temkin and a recent bound on the number of
subsets of integers with small sumset by Green and Morris. We also discuss
related results and open problems on the number of maximal sum-free subsets of
abelian groups.
