The first approach to the history of mathematics in China led by Li Yan (1892-1963) and Qian Baocong (1892-1974) featured discovering what mathematics had been done in China's past. From the 1970s on, Wu Wen-tsun and others shifted this research paradigm to one of recovering how mathematics was done in ancient China. Both approaches, however, focus on the same problem, that is mathematics in history. The theme of the third approach is supposed to be why mathematics was done. Combining this approach with the former two, the research paradigm will be improved from one of mathematics in history to that of the history of mathematics.