The ancient Chinese manuscript that transformed mathematics education

Jason Yip explains the significance and uniqueness of the Shu Li Ge Zhi (數理格致) manuscript by Li Shanlan (李善蘭), one of the earliest Chinese translations of Newton’s work, archived in the SOAS Special Collections. 

We once believed that the earth was flat and our planet was the centre of the universe. It took us quite a long while to embrace the perception of a spherical earth and the heliocentric model. Since Newton’s epoch-making discovery in the 17^th century, interpreting the physical world has finally become mathematically possible for human beings. Not only did the law of universal gravitation provide a rather convincing explanation for the movement of celestial bodies, but also for the motion of objects in our daily lives.

The development of calculus and knowledge exchange

In parallel with his scientific theory, calculus was developed, serving as the cornerstone of classical mechanics. Newton spoke of standing on the shoulders of giants. Although we cannot determine whether he was genuinely attributing his triumph to preceding scientists like Galileo and Kepler or mocking his rival Hooke, who suffered from kyphosis, what we do know is that the exchange and transmission of knowledge matter. A hundred years later, the first Chinese translation of Philosophiæ Naturalis Principia Mathematica appeared in China, known as Shu Li Ge Zhi (數理格致). Its manuscript is now in the Special Collections of SOAS Library.

The first Chinese translation of Philosophiæ Naturalis Principia Mathematica appeared in China, known as Shu Li Ge Zhi (數理格致). Its manuscript is now in the Special Collections of SOAS Library.

During the second wave of the eastward dissemination of Western learning (西學東漸), many other important mathematical treatises, such as Euclid’s Elements and De Morgan's Elements of Algebra, were translated by Alexander Wylie and Li Shanlan together in late Qing Dynasty. The former was a British Protestant Christian missionary, while the latter was the greatest Chinese mathematician of his time. In the process of introducing various contemporary mathematical topics, Li coined a great number of Chinese terminologies which remain part of his most influential legacy. 

Chinese language morphology and mathematical concepts

A few weeks ago, I delivered a talk at the British Society for the History of Mathematics Annual Meeting, highlighting some unique features in ancient Chinese mathematical texts. One of the themes in my presentation was the preciseness and conciseness of the wording. Shu Li Ge Zhi was used as an example to demonstrate how mathematical concepts could be inserted into Chinese characters.

To appreciate the elegance of Li’s work, we must first have an elementary understanding of the Chinese language from a linguistic perspective. Here, its morphology will be briefly covered. To commence, the written language in Chinese consists solely of morphemic characters. In other words, phonetics are excluded. The reason why much information can be embedded within one single character is that there exists a rich morphological structure, where individual morphemes often carry significant semantic and syntactic meaning. 

As the character-based writing is in the form of logograms, each component represents a morpheme or a word. For instance, the word 算 (count/calculate) integrates 竹 (bamboo) and 具 (tool/manipulate). Furthermore, Chinese words are often composed of multiple morphemes. The meaning of a word can be understood by investigating the corresponding morphemes. Here are a couple of examples. The word 算術 (arithmetic) comprises 算 (count/calculate) and 術 (art/technique), while 數學 (mathematics) comprises 數(number/count) and 學 (study/learn). Lastly, one may recognize a deeper meaning when the distinct morphemes complement each other well. In the word 猜想 (conjecture), it includes both 猜 (guess) and 想 (think). With all these aforementioned characteristics, knowledge delivery could be effectively executed.

The lasting influence of Shu Li Ge Zhi

Although the documentation of Li’s translation at SOAS Library is unfortunately incomplete, containing only the beginning (up to Preposition XXI, Book I) of the Principia, it is an irreplaceable artefact showing the derivation of modern Chinese mathematical terms. Some English terminologies, such as constant and horizontal axis, already consist of specific meanings. Their word-to-word translations, 常數 and 橫軸, are expected. 常 means unchangeable and 數 suggests a number, while 橫 indicates the horizon and 軸 represents an axle. 

However, what really sets Li’s work apart is how the mathematical concepts were injected into the combinations of characters, making them even more expressive than the original language. For instance, asymptotes, calculus, and logarithm were translated as 漸近線, 微積分, and 對數, respectively. For the first one, 漸近 means “to gradually become closer”, and 線 refers to a line. Secondly, 微 implies infinitesimal, 積 is equivalent to collecting, and 分 indicates parts. It is worth noticing that the word calculus is actually adopted from Latin, which was used to describe small pebbles. Lastly, 對 means “to correlate” and 數 again means numbers. Interestingly, 對數 echoes its etymological roots from Greek, which are logos (ratio) and arithmos (number).

Undoubtedly, Shu Li Ge Zhi facilitated scientific development and mathematics education in East Asia.

Undoubtedly, Shu Li Ge Zhi facilitated scientific development and mathematics education in East Asia. Apart from expanding the Chinese mathematical vocabulary, the newly coined terminologies were also borrowed in Japan. Their traces can still be found in mathematics textbooks today. All in all, what is the essence of mathematics? Some may claim it is problem-solving or proving theorems. However, mathematics also represents the human thought process, which, to me, is the most precious heritage of mankind. Through words and symbols, knowledge is transmitted from one generation to another. Let us pay homage to all the giants before us.

Header image: Shu Li Ge Zhi (數理格致) via SOAS Special Collections.