What grows well around the base of a large oak tree?

How about ferns?

you can always add potting soil if you have that as an option. we put railroad ties around ours, added the soil and placed crotans and different annual type flowers that didnt need much sun. what have you tried?

Congratulations on the tree! Large split-leaf philodendron will grow around the base and climb the trunk. Bromiliads are easy and pretty - lots of varieties. Hostas also offer light and dark leaf varieties. Calladiums will grow close to the tree if you pile in some potting soil to cover the tubers, and they can add color. They look pretty inter-planted with fern. You might try a shade-loving moss if you can find it - that is pretty on the exposed roots.

You can also plant spring bulbs which flower when the tree has no leaves and pulmonaria,hellebores etc. I find all of these successful under a tree.

A large oak tree is a treasure indeed. not that you would but can you imagine the value of that tree in terms of the wood it contains... I think it's value is better calculated by the shade it imparts the soil it anchors and the time it has taken to grow. Large, very old trees are rare anymore...
I know of a lady in Louisiana who has two extremely large oaks in her backyard and was complaining that she couldn't grow anything under them...When I pointed out their antiquity she began to think differently about her trees...she was very excited to learn that a conservative estimate of their ages..from girth only..had them as saplings at the time of the American Revolution. lol. How many people have that kind of history in their backyards?
perhaps you could contact an arborist..and have your trees ages determined and have the trees assessed for health as well. then if you need something planted below them use interesting planters and don't disturb your trees roots... Sorry I'm just an old treehugger.
congratulations
Lori