Place around hostas to deter slugs.

I have sprayed some with gold paint for Xmas decorations, but thousands is a bit much.

They keep the cats away from our beds.

Unlike conifer cones, sweetgum balls contain very little wood and their walls are rather thin, so they decompose in a compost pile under two years - especially if supplemented with nitrogen.

We have a cycle of two compost piles, one of which is replaced every year so the decomposition time for the material in a pile is between one and two years. The mature pile is distributed in the spring and a fresh one is started in its place and the first waste loaded on it are the gumballs from the previous winter. There are only minor remnants of the balls after one year, when the pile is 'closed' and no new material is being added to it any more and not even any traces of them after two years when the pile is distributed.

Good instructions,CasaLester.
Wondering how much seed sprouting you get in the fresher mulch pile and would raising the pile off the ground a bit eliminate that problem?

Periodic turning over of the pile should take care of whatever manages to sprout. Germination and subsequent killing of the sprouts appears to be preferable to letting the seeds linger in the compost and germinate later when the compost is spread. It may even be encouraged by keeping the surface of the pile moist and exposed to light. Turning over shouldn't be done too frequently (not more than every 2-3 weeks) so that there is enough time for the seeds to germinate and then to die while buried. The pile should have some volume above ground (at least 2 feet) to speed up the decomposition inside it - especially in cold seasons.