Knowing which countries contribute the most to pushing the boundaries of knowledge in science and technology has social and political importance. However, common citation metrics do not adequately measure this contribution. This measure requires more stringent metrics appropriate for the highly influential breakthrough papers that push the boundaries of knowledge, which are very highly cited but very rare. Here I used the recently described Rk index, specifically designed to address this issue. I applied this index to 25 countries and the EU across 10 key research topics, five technological and five biomedical, studying domestic and international collaborative papers independently. In technological topics, the Rk indices of domestic papers show that overall, the USA, China, and the EU are leaders; other countries are clearly behind. The USA is notably ahead of China, and the EU is far behind China. The same approach to biomedical topics shows an overwhelming dominance of the USA and that the EU is ahead of China. The analysis of internationally collaborative papers further demonstrates the US dominance. These results conflict with current country rankings based on less stringent indicators.

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