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The Boston Consulting Group (BCG) is a global management consulting firm and the world's leading advisor on business strategy. We partner with clients in all sectors and regions to identify their highest-value opportunities, address their most critical challenges, and transform their businesses. Our customized approach combines deep insight into the dynamics of companies and markets with close collaboration at all levels of the client organization. This ensures that our clients achieve sustainable competitive advantage, build more capable organizations, and secure lasting results. Founded in 1963, BCG is a private company with 66 offices in 38 countries. For more information, please visit www.bcg.com.

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Innovation is to organizations what evolution is to organisms: it is how organizations adapt to environmental change and improve. Yet despite advances in our understanding of evolution, what drives innovation remains elusive. On the one hand, organizations invest heavily in systematic strategies to accelerate innovation. On the other, historical analysis and individual experience suggest that serendipity plays a significant role. To unify these perspectives, we analysed the mathematics of innovation as a search for designs across a universe of component building blocks. We tested our insights using data from language, gastronomy and technology. By measuring the number of makeable designs as we acquire components, we observed that the relative usefulness of different components can cross over time. When these crossovers are unanticipated, they appear to be the result of serendipity. But when we can predict crossovers in advance, they offer opportunities to strategically increase the growth of the product space.

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