  Solving a decades-old problem we show that Keisler's 1967 order on theories
has the maximum number of classes. The theories we build are simple unstable
with no nontrivial forking, and reflect growth rates of sequences which may be
thought of as densities of certain regular pairs, in the sense of Szemer\'edi's
regularity lemma. The proof involves ideas from model theory, set theory, and
finite combinatorics.
