How was the dating conducted?

Method

In all, 82 samples of charcoal (from 10 to 100 milligrams each) directly taken from cave paintings, torch snuffs, and the hearths on the ground gave results statistically reliable. Carbon 14 data shows that the cave was used during two separate periods. The first period was during the Aurignacian culture, between 32,000 and 30,000 years BP. The second period was between 27,000 and 24,500 years BP, during the Gravettian culture.
Most of the cave paintings were painted during the first period. During the second period, the cave was lightly frequented, keeping the Aurignacian art intact.

Man has left his mark by spraying the pigments on a hand directly pressed against the wall