Skilling Peter. In: Arts asiatiques , tome 63, Map by Pierre Pichard. The last decades of archaeological discoveries have significantly transformed the map of Buddhist sites of ancient India. Important new stupa complexes have been excavated throughout the country1. Existing literature has yet to catch up with the new data, which, when it has been published at all, is scattered in archaeological reports and in specialized articles.

Our trusty reference works, such as Lamotte's Histoire du bouddhisme indien, first published in , or Debala Mitra's Buddhist Monuments, published in , are now very much out of date2. A stupa or caitya is a solid structure built to enshrine a casket or chamber containing the ashes and bones of a Buddha or, in some cases, of his disciples or other revered figures.

A stupa does not usually stand alone ; it is part of a complex that can include shrine-halls, image-halls, congregation- halls, refectories, and residences. Yang Hui, Qin Jiushao, Zhu Shijie all used the Horner - Ruffini method six hundred years earlier to solve certain types of simultaneous equations, roots, quadratic, cubic, and quartic equations. Yang Hui was also the first person in history to discover and prove " Pascal's Triangle ", along with its binomial proof although the earliest mention of the Pascal's triangle in China exists before the eleventh century AD.

His book; Ceyuan haijing revolutionized the idea of inscribing a circle into triangles, by turning this geometry problem by algebra instead of the traditional method of using Pythagorean theorem. Guo Shoujing of this era also worked on spherical trigonometry for precise astronomical calculations. At this point of mathematical history, a lot of modern western mathematics were already discovered by Chinese mathematicians. Things grew quiet for a time until the thirteenth century Renaissance of Chinese math.

This saw Chinese mathematicians solving equations with methods Europe would not know until the eighteenth century. The high point of this era came with Zhu Shijie 's two books Suanxue qimeng and the Siyuan yujian.

## Xuanzang (玄奘) : Buddhist records of the Western world (大唐西域記), book II.

In one case he reportedly gave a method equivalent to Gauss 's pivotal condensation. Qin Jiushao c. Referring to Qin's solution of a 4th order equation, Yoshio Mikami put it: "Who can deny the fact of Horner's illustrious process being used in China at least nearly six long centuries earlier than in Europe?

He used Tian yuan shu to convert intricated geometry problems into pure algebra problems. He then used fan fa , or Horner's method , to solve equations of degree as high as six, although he did not describe his method of solving equations. Although he did not describe his method of solution of equations, it appears that it was not very different from that used by Chu Shih-chieh and Horner.

Others who used the Horner method were Ch'in Chiu-shao ca. The four elements, called heaven, earth, man and matter, represented the four unknown quantities in his algebraic equations. It deals with simultaneous equations and with equations of degrees as high as fourteen. The author uses the method of fan fa , today called Horner's method , to solve these equations.

There are many summation series equations given without proof in the Mirror. A few of the summation series are: [40]. Shu-shu chiu-chang , or Mathematical Treatise in Nine Sections , was written by the wealthy governor and minister Ch'in Chiu-shao ca. The earliest known magic squares of order greater than three are attributed to Yang Hui fl. The embryonic state of trigonometry in China slowly began to change and advance during the Song Dynasty — , where Chinese mathematicians began to express greater emphasis for the need of spherical trigonometry in calendarical science and astronomical calculations.

Gauchet and Joseph Needham state, Guo Shoujing used spherical trigonometry in his calculations to improve the calendar system and Chinese astronomy.

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Despite the achievements of Shen and Guo's work in trigonometry, another substantial work in Chinese trigonometry would not be published again until , with the dual publication of Euclid's Elements by Chinese official and astronomer Xu Guangqi — and the Italian Jesuit Matteo Ricci — After the overthrow of the Yuan Dynasty , China became suspicious of Mongol-favored knowledge. The court turned away from math and physics in favor of botany and pharmacology.

Imperial examinations included little mathematics, and what little they included ignored recent developments. Martzloff writes:.

At the end of the 16th century, Chinese autochthonous mathematics known by the Chinese themselves amounted to almost nothing, little more than calculation on the abacus, whilst in the 17th and 18th centuries nothing could be paralleled with the revolutionary progress in the theatre of European science. Moreover, at this same period, no one could report what had taken place in the more distant past, since the Chinese themselves only had a fragmentary knowledge of that. One should not forget that, in China itself, autochthonous mathematics was not rediscovered on a large scale prior to the last quarter of the 18th century.

Correspondingly, scholars paid less attention to mathematics; pre-eminent mathematicians such as Gu Yingxiang and Tang Shunzhi appear to have been ignorant of the Tian yuan shu Increase multiply method. To the average scholar, then, tianyuan seemed numerology. When Wu Jing collated all the mathematical works of previous dynasties into The Annotations of Calculations in the Nine Chapters on the Mathematical Art , he omitted Tian yuan shu and the increase multiply method.

Instead, mathematical progress became focused on computational tools. In 15 century, abacus came into its suan pan form.

## BUDDHIST ETHICS: A BIBLIOGRAPHICAL ESSAY

Easy to use and carry, both fast and accurate, it rapidly overtook rod calculus as the preferred form of computation. Zhusuan , the arithmetic calculation through abacus, inspired multiple new works. Suanfa Tongzong General Source of Computational Methods , a volume work published in by Cheng Dawei , remained in use for over years. Although this switch from counting rods to the abacus allowed for reduced computation times, it may have also led to the stagnation and decline of Chinese mathematics.

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The pattern rich layout of counting rod numerals on counting boards inspired many Chinese inventions in mathematics, such as the cross multiplication principle of fractions and methods for solving linear equations. Similarly, Japanese mathematicians were influenced by the counting rod numeral layout in their definition of the concept of a matrix. Algorithms for the abacus did not lead to similar conceptual advances.

This distinction, of course, is a modern one: until the 20th century, Chinese mathematics was exclusively a computational science. In the late 16th century, Matteo Ricci decided to published Western scientific works in order to establish a position at the Imperial Court. With the assistance of Xu Guangqi , he was able to translate Euclid's Elements using the same techniques used to teach classical Buddhist texts. Under the Western-educated Kangxi Emperor , Chinese mathematics enjoyed a brief period of official support.

Meishi Congshu Jiyang was an encyclopedic summary of nearly all schools of Chinese mathematics at that time, but it also included the cross-cultural works of Mei Wending , Goucheng's grandfather. However, no sooner were the encyclopedias published than the Yongzheng Emperor acceded to the throne. Yongzheng introduced a sharply anti-Western turn to Chinese policy, and banished most missionaries from the Court. With access to neither Western texts nor intelligible Chinese ones, Chinese mathematics stagnated. In , the First Opium War forced China to open its door and looked at the outside world, which also led to an influx of western mathematical studies at a rate unrivaled in the previous centuries.

In , the Chinese mathematician Li Shanlan and the British missionary Alexander Wylie co-translated the later nine volumes of Elements and 13 volumes on Algebra. Chinese scholars were initially unsure whether to approach the new works: was study of Western knowledge a form of submission to foreign invaders? But by the end of the century, it became clear that China could only begin to recover its sovereignty by incorporating Western works.

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Chinese scholars, taught in Western missionary schools, from translated Western texts, rapidly lost touch with the indigenous tradition. As Martzloff notes, "from onwards, solely Western mathematics has been practised in China. Chinese mathematics experienced a great surge of revival following the establishment of a modern Chinese republic in Ever since then, modern Chinese mathematicians have made numerous achievements in various mathematical fields. In , at the beginning of the founding of New China, although the country was in a predicament of lack of funds and a lot of waste, the government paid great attention to the cause of science.

The Chinese Academy of Sciences was established in November The Institute of Mathematics was formally established in July Then, the Chinese Mathematical Society and its founding journals restored and added other special journals.

In the 18 years after liberation, the number of published papers accounted for more than three times the total number of articles before liberation. Many of them not only filled the gaps in China's past, but also reached the world's advanced level. Just as mathematicians fought to catch up and try to restore the advanced position of Chinese mathematics in the world, a ruthless storm swept China.

In the decade of the Cultural Revolution, society was out of control, people were chaotic, and science declined. In the field of mathematics, in addition to Chen Jingrun, Hua Luogeng, Zhang Guanghou and other mathematicians struggling to open a few flowers, almost full of dying, a blank. When the political disaster of 10 years passed, people looked up and the mathematics research in other countries had already peaked.

It took a lot of effort to catch up. The Chinese nation has always had a glorious tradition of self-improvement and perseverance.

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After the catastrophe, with the publication of Mr. Guo Moruo's literary "Spring of Science", the spring of mathematics has ushered in the spring of mathematics. In , a new mathematical development plan was formulated in Beijing, the work of the mathematics society was resumed, the journal was re-published, the academic journal was published, the mathematics education was strengthened, and basic theoretical research was strengthened.

An important mathematical achievement of the Chinese mathematician in the direction of the power system is how Xia Zhihong proved the Painleve conjecture in When there are some initial states of N celestial bodies, one of the celestial bodies ran to infinity or speed in a limited time. Infinity is reached, that is, there are non-collision singularities. The Painleve conjecture is an important conjecture in the field of power systems proposed in A very important recent development for the 4-body problem is that Xue Jinxin and Dolgopyat proved a non-collision singularity in a simplified version of the 4-body system around This is also an important contribution made by Chinese mathematicians.

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Other directions, such as number theory, geometric direction, Chinese mathematicians also have many important achievements. In addition, in , Shen Weixiao and Kozlovski, Van-Strien proved that Real Fatou conjecture: Real hyperbolic polynomials are dense in the space of real polynomials with fixed degree. This conjecture can be traced back to Fatou in the s, and later Smale proposed him in the s. Axiom A, and guess that the hyperbolic system should be dense in any system, but this is not true when the dimension is greater than or equal to 2, because there is homoclinic tangencies.

The work of Shen Weixiao and others is equivalent to confirming that Smale's conjecture is correct in one dimension, which is a wonderful phenomenon that belongs only to one dimension. The proof of Real Fatou conjecture is one of the most important developments in conformal dynamics in the past decade. In comparison to other participating countries at the International Mathematical Olympiad , China has highest team scores and the won the all-members-gold IMO with a full team the most number of times. Zhoubi Suanjing c. The first reference to a book being used in learning mathematics in China is dated to the second century CE Hou Hanshu : 24, ; 35, Cullen claims that mathematics, in a manner akin to medicine, was taught orally.

From Wikipedia, the free encyclopedia. History of mathematics in China. Main article: Ceyuan haijing. Britannica Online Encyclopedia. Science and Civilization in China. England: Cambridge University Press. T'oung Pao. Second Series. Swetz and T.