  The Goldman-Parker Conjecture classifies the complex hyperbolic C-reflection
ideal triangle groups up to discreteness. We proved the Goldman-Parker
Conjecture in [Ann. of Math. 153 (2001) 533--598] using a rigorous
computer-assisted proof. In this paper we give a new and improved proof of the
Goldman-Parker Conjecture. While the proof relies on the computer for extensive
guidance, the proof itself is traditional.
