Creativity is the generation of an idea or artifact judged to be novel and high-quality by a knowledgeable social group, and is often said to be the pinnacle of intelligence. Several computational creativity systems of various designs are now being demonstrated and deployed. These myriad design possibilities raise the natural question: Are there fundamental limits to creativity? Here, we define a mathematical abstraction to capture key aspects of combinatorial creativity and study fundamental tradeoffs between novelty and quality. The functional form of this fundamental limit resembles the capacity-cost relationship in information theory, especially when measuring novelty using Bayesian surprise—the relative entropy between the empirical distribution of an inspiration set and that set updated with the new idea or artifact. As such, we show how information geometry techniques provide insight into the limits of creativity and find that the maturity of the creative domain directly parameterizes the fundamental limit. This result is extended to the case when there is a diverse audience for creativity and when the quality function is not known but must be estimated from samples.