We studied the research performance of 69 countries by considering two different types of new knowledge: incremental (normal) and fundamental (radical). In principle, these two types of new knowledge should be assessed at two very different levels of citations, but we demonstrate that a simpler assessment can be performed based on the total number of papers (P) and the ratio of the number of papers in the global top 10% of most cited papers divided to the total number of papers (Ptop 10%/P). P represents the quantity, whereas the Ptop 10%/P ratio represents the efficiency. In ideal countries, P and the Ptop 10%/P ratio are linked to the gross domestic product (GDP) and GDP the per capita, respectively. Only countries with high Ptop 10%/P ratios participate actively in the creation of fundamental new knowledge and have Noble laureates. In real countries, the link between economic and scientific wealth can be modified by the technological activity and the research policy. We discuss how technological activity may decrease the Ptop 10%/P ratio while only slightly affecting the capacity to create fundamental new knowledge; in such countries, many papers may report incremental innovations that do not drive the advancement of knowledge. Japan is the clearest example of this, although there are many less extreme examples. Independently of technological activity, research policy has a strong influence on the Ptop 10%/P ratio, which may be higher or lower than expected from the GDP per capita depending on the success of the research policy.