  We give a short and direct proof of the $\lambda_g$-Conjecture. The approach
is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the
``polynomiality'' of Hurwitz numbers, from which we pick off the lowest degree
terms. The proof is independent of Gromov-Witten theory.
  We briefly describe the philosophy behind our general approach to
intersection numbers and how it may be extended to other intersection number
conjectures.
