The past few centuries have witnessed a dramatic growth in scientific and technological knowledge. However, the nature of that growth - whether exponential or otherwise - remains controversial, perhaps partly due to the lack of quantitative characterizations. We evaluated knowledge as a collective thinking structure, using citation networks as a representation, by examining extensive datasets that include 213 million publications (1800-2020) and 7.6 million patents (1976-2020). We found that knowledge - which we conceptualize as the reduction of uncertainty in a knowledge network - grew linearly over time in naturally formed citation networks that themselves expanded exponentially. Moreover, our results revealed inflection points in the growth of knowledge that often corresponded to important developments within fields, such as major breakthroughs, new paradigms, or the emergence of entirely new areas of study. Around these inflection points, knowledge may grow rapidly or exponentially on a local scale, although the overall growth rate remains linear when viewed globally. Previous studies concluding an exponential growth of knowledge may have focused primarily on these local bursts of rapid growth around key developments, leading to the misconception of a global exponential trend. Our findings help to reconcile the discrepancy between the perceived exponential growth and the actual linear growth of knowledge by highlighting the distinction between local and global growth patterns. Overall, our findings reveal major science development trends for policymaking, showing that producing knowledge is far more challenging than producing papers.