Abstract: For a long time, the academic community has generally regarded the emptiness of xinxue (i.e. school of the mind in the middle Ming dynasty) as a key factor in the decline of mathematics and even science during the Ming dynasty. Since Zhu Yuanzhang, the Taizu Emperor of the Ming Dynasty, abolished School of Mathematics at the Imperial University, scholars’ understanding of the relationship between mathematics and Confucianism was largely shaped by Zhu Xi’s influence. In the middle of the Ming Dynasty, xinxue gained prominence, with Wang Yangming considering mathematics an insignificant branch of his xinxue. However, some of his followers, such as Gu Yingxiang and Tang Shunzhi, engaged deeply traditional mathematics. As a result, there was no theoretical consensus on the relationship between mathematics and xinxue. This divergence was linked to the coexistence of multiple mathematical practices in the Jiajing reign of the Ming Dynasty. On the one hand, Gu Yingxiang, Tang Shunzhi, and Zhou Shuxue devoted considerable efforts to study problems relating to right-angle triangle as well as arc-sagitta of circles. However, since the mathematical manuscripts available at that time may not have included detailed procedural explanations using rod numerals, these scholars struggled to fully understand the operations of the Celestial Source method. On the other hand, mathematics continues to thrive in various practical domains, including commerce, military strategy and music. From the perspective of mathematical practice, mathematics and xinxue were relatively independent. The rise of xinxue did not, in itself, present a substantial obstacle to the development of mathematics and science.

Key Words: Mathematical practice; School of the Mind; Gu Yingxiang; Tang Shunzhi; Zhou Shuxue