1607, a year of (some) significance: Translation of the first European text in mathematics - Elements - into Chinese

The Italian Jesuit Matteo Ricci and the Chinese scholar-official XU Guang-qi of the Ming Dynasty collaborated to produce a translation of the first six books of Elements (more precisely, the fifteenbook-version Euclidis Elementorum Libri XV compiled by Christopher Clavius in the latter part of the fifteenth century) in Chinese in 1607, with the title Ji He Yuan Ben (Source of Quantity). This paper attempts to look at the historical context that made Elements the first European text in mathematics to be translated in China, and how the translated text was received at the time as well as what influence the translated text exerted in various domains in subsequent years, if any, up to the first part of the 20th century. This first European text in mathematics transmitted into China led the way of the first wave of transmission of European science into China, while a second wave and a third wave followed in the Qing Dynasty, but each in a rather different historical context. Besides comparing the styles and emphases of mathematical pursuit in the eastern and the western traditions the paper looks at the issue embedded in a wider intellectual and cultural context.postprin

Does Society Need IMO Medalists?

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Mathematics education in East Asia from antiquity to modern times

Since the early 1990s the learning process of Asian students brought up in the tradition of the Confucian heritage culture (CHC) has become a much discussed issue. As a consequence the teaching process of Asian teachers in CHC classrooms has attracted the same attention. These two related issues are brought into focus in the so-called “CHC Learner / Teacher Paradox”. It is therefore natural to look at the history of mathematics education in some Asian countries such as China, Japan and Korea. This paper attempts to give an account of this long episode from ancient to medieval to modern times with illustrative examples.postprin

The combinatorics of binary arrays

This paper gives an account of the combinatorics of binary arrays, mainly concerning their randomness properties. In many cases the problem reduces to the investigation on difference sets.postprin

Proof within the Western and the Eastern cultural traditions: Implications for mathematics education

Plenary Panelpostprin

Facing the change and meeting the challenge: Mathematics curriculum of Tongwen Guan in China in the second half of the nineteenth century

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On Alexander Wylie’s Jottings on the Science of the Chinese Arithmetic

Oral Presentation(Theme 2): R102Starting from August of 1852 the British Protestant missionary and sinologist, Alexander Wylie (1815–1887), published in nine instalments an account Jottings on the Science of the Chinese Arithmetic in the newspaper North China Herald. He explained clearly the purpose of his account at the beginning: ‘The object of the following desultory notes, made from time to time, in the course of some researches entered upon, with another purpose in view, is to draw attention to the state of the arithmetical science in China, a subject which has not been so fully explored as it might with advantage, and on which some erroneous statements have been current in modern publications.’ Alexander Wylie is a well-known figure in the last quarter of the Qing Dynasty for his contribution in transmitting Western science into China during the latter half of the 19th century. In mathematics he was known for translating three treatises in collaboration with the Qing mathematician Li Shanlan (1811–1882) — Supplementary Elements of Geometry in 1856 but published in 1865 (believed to be based on the English translation of Book VII to XV of Elements by Henry Billingsley in 1570), Treatise of Algebra in 1859 (based on Elements of Algebra by Agustus De Morgan in 1835) and Analytical Geometry and Differential and Integral Calculus Step by Step in 1859 (based on Elements of Analytical Geometry and of the Differential and Integral Calculus of Elias Loomis in 1850). He was also the author of Compendium of Arithmetic published in 1853. This presentation will discuss the knowledge of Chinese science and mathematics which most European sinologists of the 18th and 19th centuries possessed and the low regard they held it in, but the viewpoint of which was critically examined by Wylie in his account.published_or_final_versio

An inequality between the diameter and the inverse dual degree of a tree

Let T be a nontrivial tree with diameter D(T) and radius R(T). Let I(T) be the inverse dual degree of T which is defined to be , where for uV(T). For any longest path P of T, denote by a(P) the number of vertices outside P with degree at least 2, b(P) the number of vertices on P with degree at least 3 and distance at least 2 to each of the end-vertices of P, and c(P) the number of vertices adjacent to one of the end-vertices of P and with degree at least 3. In this note we prove that . As a corollary we then get with equality if and only if T is a path of at least four vertices. The latter inequality strengthens a conjecture made by the program Graffiti.postprin

Combinatorics and algebra: A medley of problems? A medley of techniques?

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Chinese Arithmetic in the Eyes of a British Missionary and Calculus in the Eyes of a Chinese Mathematician: Collaboration between Alexander Wylie (1815-1887) and LI Shan-Lan (1811-1882)

Workshop(Theme 3), R102: Original sources in the classroom, and their educational effectsThis workshop, which supplements and complements a presentation by the same authors titled ‘On Alexander Wylie’s Jottings on the Science of the Chinese Arithmetic’, will focus on several works of Wylie and Li Shan-lan. Through working together on relevant passages taken from these and related primary sources we try to see how equations were treated in traditional Chinese mathematics in comparison with Western techniques and how nineteenth century Chinese learnt calculus as a newly introduced subject with new symbols and terms to be translated and coined. We would also try to see whether we can relate the study to the modern context, especially in the classroom context.published_or_final_versio