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I came across this from the Wiki article on Chinese Mathematics:

After the overthrow of the Yuan Dynasty, China became suspicious of knowledge it used. The Ming Dynasty turned away from math and physics in favor of botany and pharmacology.

There's no citation. Is that really true? Were there any decrees by the emperor about it? To what extent did China shun math and physics?

  • The answers seem to be in the next two paragraphs on the same page. Which part of "many works devoted to abacus mathematics appeared in this period; at the expense of new idea creation." strikes you as unclear? The source for that almost certainly is one or both of the two books on the history of computing that are cited on the paragraph that brings up abacuses. Or Needham, Joseph (1986). – Denis de Bernardy Jun 6 '18 at 9:40
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    @DenisdeBernardy That's not an answer in any way, let alone a self-evident answer. Devotion to translating rod calculus to abacus calculus has nothing to do with shunning math or physics, or Mongols. Are you perhaps saying, the rise of abacus and the shunning of Mongols, were not coincidences? Did the Chinese suddenly see rod calculus as "Mongolian"? Thus spurring an alternative? Seems highly unlikely. The Chinese had both rods and abacus well before the Yuan Dynasty. If you know contrary evidence, please share it. In any case, it has absolutely nothing to do with the "shunning physics" part. – DrZ214 Jun 6 '18 at 10:36
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    @DenisdeBernardy - Kind of with the poster on this one. It does go on to say that the abacus being so great might have had something to do with loss of interest in math as well, but it doesn't address the other reasons claimed in the quoted passage at all, and certainly doesn't say anything about botany (unless there's some well-known abacus-botany connection I'm unaware of). – T.E.D. Jun 6 '18 at 14:12
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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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    Splendid answer. – Mark C. Wallace Jun 7 '18 at 17:45
  • The answer is interesting but I'm not sure what to make of it. Is it: We don't really know because we didn't really study it but there were actually some hot stuff in there? Or is it: Indeed, they were stuck into developments with abacuses and a few other minor things while Europeans were developing modern algebra and calculus? If the former it would be sweet to flesh out what the hot stuff was. What did they actually figure out on their own or import from abroad during the Ming period and later. – Denis de Bernardy Jun 7 '18 at 18:54
  • This is a detailed answer, but I can't help but notice the "physics part" is lacking. Did the Ming really turn away from physics? (as compared to the Yuan or Song). – DrZ214 Jun 7 '18 at 22:01
  • @DenisdeBernardy : The second (stuck into minor things) has been the “fairly unanimous” position of scholars for decades, if not centuries. In said book, Roger Hart says this position is self sustaining, de facto preventing studies of Ming science. Its purported explanations are inconsistent with evidences, and the definition of “minor things” is biased by our knowledge of the future. Earlier in the book, he draws a parallel with Newton’s alchemy, which Newton thought to be more important that his work on gravitation and optics. – Frédéric Grosshans Jun 8 '18 at 8:06
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    In other words, the traditional explanation says it is not even worth exploring, so no one has explored the area, which is taken as an evidence there is nothing (a bit like the traditonal view of western middle-ages vs Renaissance). One needs an investigation to have teh precise examples of Ming accomplishments you ask for (beyond Zhu Zaitu‘s work (comparison of base 10 vs base 9 numeral systems, equal temperament scale, 25 decimal computation methods), which happened precisely in the kind of environment the traditional explanations says is the most hostile to creativity) – Frédéric Grosshans Jun 8 '18 at 9:54

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