By the 19th century, the splendor of Chinese mathematics was long gone. To close what had become a considerable gap with the West, China embarked on the immense task of translating, adapting and developing Western mathematics. This inevitably sparked numerous debates, including within the Chinese scientific community. After all, China could claim to have preceded the West in many areas of mathematics, so why should China be the one to adapt? Some also believed that Western developments were merely deductions from achievements already known in ancient China. Others, however, acknowledged that China had fallen behind and needed to take pragmatic steps to catch up. Mathematics thus became a highly political issue, creating friction between conservatives and modernizers.
Western notation could, of course, generally be introduced by adapting it to Chinese numerals and the existing symbolism, and for the most part this went smoothly—mathematics fully deserved its reputation for universality. Fractions, however, posed a more serious problem, since they were written in the reverse order from Western notation: "three twelfths" was written not as 3 / 12 but as 12 / 3!
This notation reflected the structure of the language. In Chinese, "three twelfths" is said—that is, pronounced—"of twelve parts, three." It therefore made more sense to write the denominator first and the numerator second, following the order in which the expression was spoken. At a time when the colonial powers posed a growing threat, this also provided an opportunity for nationalist assertion.
One prominent advocate of retaining Chinese notation—not only for fractions but also, more generally, for the use of Chinese rather than Hindu-Arabic numerals—was John Fryer (1838–1923), head of the translation department at the Jiangnan Arsenal, at a time when the Chinese government relied on mathematical research chiefly for military and naval purposes. Fryer, however, was one of only a few translators of the period to take this position, which ultimately proved less persuasive than the fear that China might become isolated from the rest of the world. Imported conventions therefore gradually prevailed, including the Western way of writing fractions.
The main lesson from this brief anecdote is that mathematical notation, despite its apparent political neutrality, can in fact become a significant factor in cultural and geopolitical dynamics.