  The growth of science and technology is a recombinative process, wherein new
discoveries and inventions are built from prior knowledge. Yet relatively
little is known about the manner in which scientific and technological
knowledge develop and coalesce into larger structures that enable or constrain
future breakthroughs. Network science has recently emerged as a framework for
measuring the structure and dynamics of knowledge. While helpful, existing
approaches struggle to capture the global properties of the underlying
networks, leading to conflicting observations about the nature of scientific
and technological progress. We bridge this methodological gap using tools from
algebraic topology to characterize the higher-order structure of knowledge
networks in science and technology across scale. We observe rapid growth in the
higher-order structure of knowledge in many scientific and technological
fields. This growth is not observable using traditional network measures. We
further demonstrate that the emergence of higher-order structure coincides with
decline in lower-order structure, and has historically far outpaced the
corresponding emergence of higher-order structure in scientific and
technological collaboration networks. Up to a point, increases in higher-order
structure are associated with better outcomes, as measured by the novelty and
impact of papers and patents. However, the nature of science and technology
produced under higher-order regimes also appears to be qualitatively different
from that produced under lower-order ones, with the former exhibiting greater
linguistic abstractness and greater tendencies for building upon prior streams
of knowledge.
