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.