  Scientific fields differ in terms of their subject matter, research
techniques, collaboration sizes, rates of growth, and so on. We investigate
whether common dynamics might lurk beneath these differences, affecting how
scientific fields form and evolve over time. Particularly important in any
field's history is the moment at which shared concepts and techniques allow
widespread exchange of ideas and collaboration. At that moment, co-authorship
networks show the analog of a percolation phenomenon, developing a giant
connected component containing most authors. We develop a general theoretical
framework for analyzing finite, evolving networks in which each scientific
field is an instantiation of the same large-scale topological critical
phenomenon. We estimate critical exponents associated with the transition and
find evidence for universality near criticality implying that, as various
fields approach the topological transition, they do so with the same set of
critical exponents consistent with an effective dimensionality $d \simeq 1$.
These results indicate that a common dynamics is at play in all scientific
fields, which in turn may hold policy implications for ways to encourage and
accelerate the creation of scientific and technological knowledge.
