Figure 1. Exponential growth in scientific knowledge.

(A) Empirically-derived exponential growth in mathematical knowledge as measured by the number of published abstracts in mathematics from 1868–1965. The curve shown is a best-fit to data reported in May [17], regression equation n = 1400e^{0.025(t-1880)}. (B) Price [12] argues that exponential increases in scientific output such as those documented by May (dashed line) are actually the initial part of a logistic growth rate (solid line), eventually reaching a saturation point due to constraints on cumulative cultural evolution.