  In 1986 Cappelli, Itzykson and Zuber classified all modular invariant
partition functions for the conformal field theories associated to the affine
$A_1$ algebra; they found they fall into an A-D-E pattern. Their proof was
difficult and attempts to generalise it to the other affine algebras failed --
in hindsight the reason is that their argument ignored most of the rich
mathematical structure present. We give here the "modern" proof of their
result; it is an order of magnitude simpler and shorter, and much of it has
already been extended to all other affine algebras. We conclude with some
remarks on the A-D-E pattern appearing in this and other RCFT classifications.
