Before revision:  We derive a theory of innovationin which products are composed of components and new components are adopted one at a time.
After 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 new components are adopted one at a time.