In the middle and late Tang Dynasty, the social crisis was increasing day by day, and the scale of Chinese studies was shrinking day by day, showing an image of being left out. Mathematics, astronomy and medical schools have been hit harder. At this time, because the imperial examination system still exists, some scholars with rich living conditions began to teach privately as a supplement to the decline of the school. After the Tang Dynasty, after five dynasties and ten countries to the Song Dynasty, private academies came into being. At the same time, the research of arithmetic, astronomy and medicine also spread to the periphery of the imperial court and the private activities of middle and high-level officials and intellectuals in society.