They are proof that you can have an agriculturally mature, technologically sophisticated eusocial self-organized system that will last for 100 million years. In contrast, humans have been a primarily agricultural species for less that 15,000 years, and our methods are demonstrably unsustainable. We could stand to learn a lot from the ants.
The ants solve their problems by tagging their environment with rich information about their own history. Our own technological situation is starting to give us the ability to do the same for human contexts, and we're working to make that augmentation explicit.
If you are interested in ants, Deborah Gordon's TED talk is an endless source of inspiration. http://www.youtube.com/watch?v=ukS4UjCauUs
What will humans do with ant superpowers? I can't wait to find out =)