Invention has been commonly conceptualized as a search over a space of combinatorial possibilities. Despite the existence of a rich literature, spanning a variety of disciplines, elaborating on the recombinant nature of invention, we lack a formal and quantitative characterization of the combinatorial process underpinning inventive activity. Here, we use US patent records dating from 1790 to 2010 to formally characterize invention as a combinatorial process. To do this, we treat patented inventions as carriers of technologies and avail ourselves of the elaborate system of technology codes used by the United States Patent and Trademark Office to classify the technologies responsible for an invention's novelty. We find that the combinatorial inventive process exhibits an invariant rate of 'exploitation' (refinements of existing combinations of technologies) and 'exploration' (the development of new technological combinations). This combinatorial dynamic contrasts sharply with the creation of new technological capabilities - the building blocks to be combined - that has significantly slowed down.We also find that, notwithstanding the very reduced rate at which new technologies are introduced, the generation of novel technological combinations engenders a practically infinite space of technological configurations.