Before revision:  There is a tension between a managerial school, which seeks a systematic prescription for innovation, and a visionary school, which ascribes innovation to serendipity and the intuition of great minds. We therefore provide a mathematical foundation for innovation---in which products are made of components and components are acquired one at a time---which serves as a common framework for both. We apply our model to data from language, gastronomy and technology.
After revision:  On the one URLanizations invest heavily in systematic strategies to drive innovation. On the other, historical analysis and individual experience suggest that serendipity plays a significant role in the discovery process. To unify these two perspectives, we analyzed the mathematics of innovation as a search process for viable designs across a universe of building blocks. We then tested our insights using historical data from language, gastronomy and technology.