50 3. MATHEMATICAL CULTURES IIThe Byzantine Empire and modern Greece. Mathematics continued in the Byzan-
tine Empire until the Turks conquered Constantinople in 1453. Of several figures
who contributed to it, the one most worthy of mention is the monk Maximus
Planudes (ca. 1260-1310), who is best known for the literature that he preserved
(including Aesop's Fables). Planudes wrote commentaries on the work of Diophan-
tus and gave an account of the Hindu numerals that was one of the sources from
which these numerals eventually came down to us (Heath, 1921, pp. 546-547).
The mainland of Greece was partitioned and disputed among various groups
for centuries: the Latin West, the Byzantine Empire, the Ottoman Empire, the
Venetians, and the Normans invaded or ruled over parts of it. In the fourteenth
century it became a part of the Ottoman Empire, from which it gained independence
only in the 1820s and 1830s. Even before independence, however, Greek scholars,
inspired by the great progress in Europe, were laying the foundations of a modern
mathematical school (see Phili, 1997).
2. Japan
Both Korea and Japan adopted the Chinese system of writing their languages. The
Chinese language was the source of a huge amount of technical vocabulary in Korea
and Japan over many centuries, and even in recent times in Viet Nam (Koblitz,
1990, p. 26). The establishment of Buddhism in Japan in the sixth century increased
the rate of cultural importation from China and even from India.^4
The influence of Chinese mathematics on both Korea and Japan was consider-
able. The courses of university instruction in this subject in both countries were
based on reading (in the original Chinese language) the Chinese classics we discussed
in Chapter 2. In relation to Japan the Koreans played a role as transmitters, pass-
ing on Chinese learning and inventions. This transmission process began in 553-554
when two Korean scholars, Wang Lian-tung and Wang Pu-son, journeyed to Japan.
For many centuries both the Koreans and the Japanese worked within the system of
Chinese mathematics. The earliest records of new and original work in these coun-
tries date from the seventeenth century. By that time mathematical activity was
exploding in Europe, and Europeans had begun their long voyages of exploration
and colonization. There was only a brief window of time during which indigenous
mathematics independent of Western influence could grow up in these countries.
The following synopsis is based mostly on the work of Mikami (1913), Smith and
Mikami (1914), and Murata (1994). Following the usage of the first two of these
sources, all Japanese names are given surname first. A word of caution is needed
about the names, however. Most Chinese symbols (kanji in Japanese) have at least
two readings in Japanese. For example, the symbol read as chu in the Japanese
word for China (Chugoku), is also read as naka (meaning middle) in the surname
Tanaka. These variant readings often cause trouble in names from the past, so that
one cannot always be sure how a name was pronounced. As Mikami (1913, p. viii)
says, "We read Seki Kowa, although his personal name Kowa should have been
read Takakazu." Several examples of such alternate readings will be encountered
below. A list of these names and their kanji rendering can be found in a paper of
Martzloff (1990, p. 373).
(^4) The Japanese word for China—Chugoku— means literally Midland, that is, between Japan and
India.