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This paper analyzes the social conditions for the prosperity of traditional mathematics in China during the Song and Yuan Dynasties.
There are three climaxes of the development of classical mathematics in the history of China. Han Dynasty, Wei, Jin, Southern and Northern Dynasties, Song and Yuan Dynasties.

The reasons for the prosperity of mathematics in Song and Yuan Dynasties are the transformation of productive forces, the development of economy, the promotion of science and technology, the rulers' attention to mathematics and the influence of the neo-Confucianism culture of "learning from others" in Song Dynasty.