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While science is presumed to be a global and open exchange of ideas, it is also increasingly complex. Collaborations more commonly transcend national borders, and more research is being produced now than at any point in history. Nations have a vested interest in science, as national influence in science is often a proxy for economic and military prowess on the international stage. However, growing economic inequality might suggest that science is increasingly less open and influenced mostly by the major powerbrokers on the international stage, which may ultimately inhibit scientific progress. Yet to date there is no consensus as to how to measure this scientific influence. The availability of large-scale publication data and the advent of computationally text analysis techniques, such as topic models, avail us the opportunity to uncover hidden patterns within scientific publications, where scientific knowledge is introduced, debated, and accepted. We also argue that it encodes a variety of subtle influences from authors spread out across different nations. To this end, we apply nation-labeled LDA topic models to over 20 million scientific paper abstracts to generate 2,142 networks of international linguistic exchanges across 126 fields and nearly 20 years of publication data. We find that the most influential ideas increasingly and exclusively emerge from an elite group of countries that includes the United States, China, and those in Western Europe. We find that the percent of GDP allocated to research and development (R&D) is what primarily drives influence across fields, even when controlling for common alternative explanations such as national power, citations, coauthoring, publishing, and proximity.