One of the charms of mathematics is the contrast between its generality and its applicability
to concrete even everyday problems. Branching processes are typical in this. Their niche of
mathematics is the abstract pattern of reproduction sets of individuals changing size and
composition through their members reproducing in other words what Plato might have called the
pure idea behind demography population biology cell kinetics molecular replication or
nuclear ?ssion had he known these scienti?c ?elds. Even in the performance of algorithms for
sorting and classi?cation there is an inkling of the same pattern. In special cases general
properties of the abstract ideal then interact with the physical or biological or whatever
properties at hand. But the population or bran- ing pattern is strong it tends to dominate
and here lies the reason for the extreme usefulness of branching processes in diverse
applications. Branching is a clean and beautiful mathematical pattern with an intellectually
challenging intrinsic structure and it pervades the phenomena it underlies.
