  We give a brief summary of some of our work and our joint work with Stephan
Tillmann on solving Thurston's equation and Haken equation on triangulated
3-manifolds in this paper. Several conjectures on the existence of solutions to
Thurston's equation and Haken equation are made. Resolutions of these
conjecture will lead to a new proof of the Poincar\'e conjecture without using
the Ricci flow. We approach these conjectures by a finite dimensional
variational principle so that its critical points are related to solutions to
Thurston's gluing equation and Haken's normal surface equation. The action
functional is the volume. This is a generalization of an earlier program by
Casson and Rivin for compact 3-manifolds with torus boundary.
