Creativity is central to the arts and sciences – and even to the human condition. The question of whether, and if so how, AI can achieve it is crucial for understanding ourselves and our AI futures – a matter we have discussed in TEDx talks. Working alongside creative practitioners, we are exploring the role of AI in scientific discovery (via neural, symbolic and neuro-symbolic modelling), the aesthetics of AI artworks, whether LLMs can understand and make genuinely creative use of language, and other key questions; and we have developed a prototype automated theorem prover.