Long historical trends in scientific discovery led mid-20th century scientometricians to mark the advent of "big science"--extensive science production--and predicted that over the next few decades, the exponential growth would slow, resulting in lower rates of increase in production at the upper limit of a logistic curve. They were wrong. This article discusses the progression and contributing factors of the growth of scientific publications. A new systematic estimate of the number of worldwide science publications from 1900-2011 shows that "big science" was transformed by unprecedented production beginning just after mid-century with no decline or slowing of exponential growth up to today. Two contrasting concurrent trends--rising competition across nations and international collaboration among scientists--have facilitated this remarkable growth. The analysis of millions of Science Citation Index Expanded (SCIE) publications shows that the number of research papers published in scientific journals over the 20th century grew rapidly. Starting from slightly below 10,000 in 1900, the annual number of new SCIE publications grew to about 50,000 in 1955. This early trend, often referred to as "big science," was then transformed into what can be called "mega global science." An exponential annual growth rate of 3.49 percent between 1980 and 2011 led to half a million SCIE publications in 1990 and approximately 1.1 million new SCIE publications in the year 2011 alone. In 1980, only about 2 percent of all SCIE publications were internationally collaborative, and just three decades later, this proportion has climbed eleven times. Currently, over one in five papers are internationally collaborative, and are driven by rising exchanges, the dominance of the English language, and Internet-based networks. Research and development requires investment not only in individuals within organizations, but also in the networks, connections, and exchanges that facilitate discoveries. Competition is complemented by collaboration.