After the Mongol Empire fell, did China really turn away from math and physics?
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TL;DR
According to Roger Hart [1], this view is widely held but wrong. He cites, among (many) others, Needham who speaks of a decay and Mikami who considers Ming scholars to be degenerate. The alleged reason is not a decree, but societal and technical characteristics of the society. This view is slow to revert, because almost no one studies Ming mathematics, because it is already known to be uninteresting.
He thinks that the Progress vs decline characterization of Yuan and Ming mathematics is anahronistic, and prevents us to understand the texts in their original context. Sepcifically, very interesting maths are overlooked in Yuan and Ming texts because of this.
Long explanation
In the 4th chapter of his book, Imagined Civilizations: China, the West, and Their First Encounter (John Hopkins, 2013, ISBN: 9781421406060), Roger Hart says that this “decline” fits with a traditional (Qing, then western) description of the Ming dynasty as a period of moral and intellectual decline. There have been works in various fields (e.g. economics) showing this view was wrong, but apparently very few in science until very recently.
On mathematics, he says this view was “fairly unanimous”, a characterization he justifies by citing many scholars: Ulrich Librecht, Li and Du, Mei, Qian Baocong, Qin Jushao, Liu Diun, Nathan Sivin, Jean-Claude Martzloff, Catherine Jami, Needham, and Mikami.
According to this view, (which Roger Hart does not share):
Crucial mathematical techniques (like root extraction, algebraic techniques based on counting rods) wer lost
Crucial treaties (Among them The nine chapters (九章算術), The Ten Mathematical Classics 算經十書) where then lost or forgotten
No great works was accomplished, or actually no work at all except on some subjects (commercial maths with the abacus, maths for music)
The needed creativity was limited by the Cheng-Zhu orthodoxy and civil service examinations, leading scholars to have only a superfical knowledge of mathematics
Science were disdained by the followers of the philosopher Wang Yangming
There was a lack of problem with heuristic signifiance, maybe because of the power of the abacus (largely enough for most uses, too limited for new techniques)
Sivin in [2] sees the abacus efficiency as helping the merchants, but too limited for the scholars, and holding back mathematics in the process. (What he sees as a) “hiatus [in mathematics developpent] may have been [according to Sivin] the price paid for by the abacus”
However, Roger Hart says that this view is not based on a study of Ming mathematics, and can’t be, since there are very few study of Ming mathematics, and the existing one are overlooked. And, of course, there are few study, because Ming mathematics is already known not to be worthy of study.
He does not think speaking of a “decline” is useful to understand what happens historically, and that many of the above view is implicitly due to an anachronistic analysis of Chinese texts, trying to see them as steps towards modern mathematics. He cites a Yuan dynasty work (Li Ye’s Sea Mirror of Circle Measurements) celebrated for his exposure of polynomial equations, and shows they are not so important in this text, especially given the Nine Chapters. However, this text rises other interesting questions (on the geometrical nature of the methods involved, Pythagorean triples, exhaustivity of the method). He also analyses two Ming dynasty books, (Cheng Dawei’s Comprehensive Source of Mathematical Methods and Zhu Zaiyu’s Records of Music), showing a certain vitality of Ming mathematics. The first hinting at a high interest in mathematics in the Ming society predating the translations of Western mathematics, and the second showing that even elements considered as cause of the “decline” (a highly conservative society, the abacus) could inspire original mathematical works (equal temperament scale precise to the 25th digit).
Bibliography
[1] Roger Hart, Imagined Civilizations: China, the West, and Their First Encounter (John Hopkins, 2013, ISBN: 9781421406060)
[2] “Science and Medicine in Chinese History,” in Heritage of China: Contemporary Perspectives on Chinese Civilization, ed. Paul S. Ropp (Berkeley: University of California Press, 1990) NAthan Sivin’s citation
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