  In the film Good Will Hunting, the main character, a janitor at MIT named
Will Hunting, attacks the problem of drawing all the homeomorphically
irreducible trees with 10 vertices. Although the film suggests that this is a
difficult problem, it is in fact quite easy. A much more interesting problem is
counting homeomorphically irreducible trees with $n$ vertices for all $n$, a
feat accomplished by Harary and Prins in 1959. Here we give an exposition and
simplification of Harary and Prins's result, introducing some of the
fundamental ideas of graphical enumeration.
