What are some low-maintenance flowers to plant in the shade under a tree?

Hostas really are the champions of low-maintenance plants, I completely agree. But if you want variety, I can suggest a few more besides what's already been mentioned - hellebores, pulmonaria, or wood geranium. Geranium is especially nice - it flowers beautifully, has decorative foliage, and doesn't spread aggressively like periwinkle does. Lily of the valley, by the way, really does take over with its persistence, but keep in mind that they can conquer the entire area under the tree if you don't keep them in check. Over time they get really dense, and it becomes almost impossible to weed anything out afterward.

The main thing to remember when planting under a tree is the roots. People often forget that old trees seriously dry out the soil and create stiff competition for young plants. Before planting, I usually add plenty of compost and peat to improve the soil at least a bit. And at first, especially if summer is dry, you need to water well until the plants are established. After that, if you choose the right types, they'll manage on their own.

One more thing - if the shade under the tree is very dense and the soil is almost black from moisture, even low-maintenance plants can start to rot. In those conditions, it's better to forget about flowers altogether and use decorative ferns or moss instead. They feel right at home there.

I'll add to the tips about hostas and periwinkle - I planted solomon's seal under an old apple tree ages ago, and it just works wonders in the densest shade. Delicate stems with little white flowers, totally unpretentious, spreads without being aggressive, but confidently takes up its space. Another great option is astilbe, especially if it's a bit damper under the tree - the foliage is lacy, it flowers for a long time, and it actually needs the shade so it doesn't fade in the sun.