The ongoing AI revolution is transforming human-computer interaction. But not all interaction is good: generative AI has made it easy to create fake data: images, news, and soon videos. But what is a fake? Can we define it mathematically? Which fakes can we detect and which cannot? I will suggest a simple probabilistic framework, where these questions can lead to concrete open (and fun!) problems in mathematics. This talk is based on a joint work with Shahar Mendelson and Grigoris Paouris: https://arxiv.org/abs/2410.18880