This is a more interesting option to climb up the crest than following the standard trail from Lake George. Begin by climbing one of the routes on Crystal Crag, then descend the South Ridge of the crag (class 3).
From the low point on the ridge extending south from Crystal Crag, you have a number of options to continue south to gain the Mammoth Crest. The most attractive route is to continue following the ridge that connects to Crystal Crag. This ridge kind of craps out at the saddle, but it is the obvious (climber's) left-to-right snaking ridge that leads up to the peaklet immediately south of Crystal Crag. It can be seen in this photo.
If the ridge is religiously followed, this is probably the spiciest alternative. However, it is fairly easy to slide off to some sand gullies on the right side if the scrambling becomes too much for you. You can also take the sand gullies all the way up, but this is pretty tedious slogging. The gullies are also visible in the photo linked above.
Farther to climber's right, you can climb up the broad, sandy chute almost due west of Crystal Crag. Near the top you will likely run into a big horizontal snowfield with remnants of a cornice. In winter, this cornice grows into a monstrosity that locals call "Jaws". Ascend to either side of the snowfield to gain the crest.
Once atop the crest, hang a left and walk along the amazingly flat ridgetop towards the highpoint.
If you have information about this route that doesn't pertain to any of the other sections, please add it here.