  The pursuit of knowledge is the permanent goal of human beings. Scientific
literature, as the major medium that carries knowledge between scientists,
exhibits explosive growth during the last century. Despite the frequent use of
many tangible measures, such as citation, impact factor and g-index, to
quantify the influence of papers from different perspectives based on
scientific productivity, it has not yet been well understood how the
relationship between scientific productivity and knowledge amount turns out to
be, i.e., how the knowledge value of papers and knowledge amount vary with
development of the discipline. This raises the question of whether high
scientific productivity equals large knowledge amount. Here, building on rich
literature on academic conferences and journals, we collect 185 million
articles covering 19 disciplines published during 1970 to 2020, and establish
citation network research area to represent the knowledge flow from the authors
of the article being cited to the authors of the articles that cite it under
each specific area. As a result, the structure formed during the evolution of
each scientific area can implicitly tells how the knowledge flows between nodes
and how it behaves as the number of literature (productivity) increases. By
leveraging Structural entropy in structured high-dimensional space and Shannon
entropy in unstructured probability space, we propose the Quantitative Index of
Knowledge (KQI), which is taken as the subtraction between the two types of
entropy, to reflect the extent of disorder difference (knowledge amount) caused
by structure (order). With the aid of KQI, we find that, although the published
literature shows an explosive growth, the amount of knowledge (KQI) contained
in it obviously slows down, and there is a threshold after which the growth of
knowledge accelerates...
