# The mathematical structure of innovation

A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.

Despite our familiarity with specific technologies, the origin of new technologies remains mysterious. Are new technologies made from scratch, or are they built up recursively from new combinations of existing technologies? To answer this, we introduce a simple model of recursive innovation in which technologies are made up of components and combinations of components can be turned into new components—a process we call technological recursion. We derive a formula for the extent to which technological recursion increases or decreases the likelihood of making new technologies. We test our predictions on historical data from three domains and find that technologies are not built up from scratch, but are the result of new combinations of existing technologies. This suggests a dynamical process by which known technologies were made and a strategy for accelerating the discovery of new ones.

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