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Endo Toshisada, Founder of the History of Japanese Mathematics As a New Field of Study: a Defeated Fighter’S Footsteps from the Battle of Ueno in 1868

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Endo Toshisada, Founder of the History of Japanese Mathematics As a New Field of Study: a Defeated Fighter’S Footsteps from the Battle of Ueno in 1868 四日市大学論集 第 32 巻 第 2 号 （The Journal of Yokkaichi University, Vol.32 No.2, 2020） Endo Toshisada, Founder of the History of Japanese Mathematics as a New Field of Study: A Defeated Fighter’s Footsteps from the Battle of Ueno in 1868 ＊ Seisho YOSHIYAMA Abstract: Endo Toshisada ( 遠藤利貞，1843-1915) was a warrior of the Kuwana Domain (around the present-day Kuwana City, Mie Prefecture), but also mathematics teacher. During the Meiji Restoration, he fought in the Battle of Ueno on the side of the “Shogitai” ( 彰義隊 ), resisting the Meiji government forces. He escaped from Edo (the present-day Tokyo), and returned to the Kuwana. In 1896, he published “A History of Mathematics of Great Japan”, this was the first book in the world on the history of Japanese mathematics. With it, Endo aspired to develop a new field of the history of traditional Japanese mathematics. Keywords: Wasan (traditional Japanese mathematics), Yozan (Western mathematics) Tokugawa Shogunate (Tokugawa Bakufu), Samurai (warrior), Domain (han), Domain warrior (hanshi), Domain school (Hankou) Introduction Endo Toshisada (1843-1915), was a warrior of the Kuwana Domain. In his early years, he received an education in Chinese literary classics, military arts and the traditional Japanese mathematics (Wasan), became a Wasan teacher. Immediately following the Meiji Restoration, he fought in the Battle of Ueno (in Edo, the present-day Tokyo) on the side of the Shogitai ( 彰義隊 , see below, section III-1) resisting the Meiji government forces. After the defeat of the Shogitai side, he managed to escape Edo and returned to the Kuwana Domain. Then, in 1877, after several years of studying and teaching Yozan (the Western mathe- matics), he started to rethink Wasan historically. In 1896, he published “A History of Mathematics of Great Japan”, which can be regarded as the first book in the world on the ＊ Aka: Qingxiang Wang, Faculty of Environmental and Information Sciences, Yokkaichi University. 71 （269） Endo Toshisada, Founder of the History of Japanese Mathematics as a New Field of Study: A Defeated Fighter’s Footsteps from the Battle of Ueno in 1868 history of Japanese mathematics. In other words, he was developing the history of tradi- tional Japanese mathematics as a new field of study. In this paper, I will make it clear that how he founded the historical science of Japa- nese mathematics and the social background (1). I. From Horio to Endo Endo Toshisada was born in 1843 as the third son of the Kuwana Domain warrior Naosaemon Toshichiri Horio at the feudal Domain’s residence in Hacchoubori, Edo (the present-day Tokyo). Shortly after that, along with his biological father, he was adopted into the Endo family, another warrior household to the Kuwana Domain. 1. The practice of adoption in feudal Japan society It is said that human first appeared in Japan about 30,000 years ago, its first Imperial court (the Yamato court) was established during the end of 4th-the beginning of 5th cen- tury. In the 12th century, Japan’s first military government was established, that is the Kamakura Shogunate or Kamakura Bakufu. Under this new political system, the Shogun was the effective ruler of the country, encharged with the Shogunate hold the administra- tion of Japan in the name of the Emperor. As in most feudal establishment, the Shogun’s position was inheritable by his sons, creating an imperative need to continue male line for the purposes of the inheritance and succession. To ensure succession, they often had to adopt a male child from another branch of the same ruling family as an heir. In the Edo period, the practice of adoption became more widespread with the introduction within the Shogunate of Domain system. Tokugawa Ieyasu received the title of Shogun from the Emperor in 1603, and promptly established the Tokugawa Shogunate. In par- ticular, as an effective way of reinforcing his power, he introduced the Shogunate Domain system. Continuing a practice that had grown up out of military alliances in the decades before, he divided the country’s land into Domains, which he allotted to his own descendants or allies, who were thus transformed into loyal Tokugawa retainers, empowered as dependent feudal lords to rule the lands. Not only the position of the Shogun and his immediate leading vassals, but also the ranks and the land possessions of the Domain lords and their dependent warriors (Samurai) were by now hereditary. The practice of adoption thus naturally became general among Samurai class families in the Edo period. Actually, the practice did not end until the Meiji period in Japan and in business families and families of politicians continues to the present-day. 72 （270） 2. Endo Toshisada’s family story Endo Toshisada’s personal story started with the Horio. Horio Yoshiharu was born in Owari Province in 1544. His father Horio Yasuharu (Yoshihisa) was from a powerful family in the region, and served Oda Nobuyasu as an influential retainer (2). Yoshiharu had previously also served Oda Nobuharu and Toyotomi Hideyoshi, before becoming lord of the Hamamatsu and the Matsue Castles. Horio Tadauji, Yoshiharu’s son, became the senior commander of the Matsue Castle in 1602, and then became the Castle lord. Tadauji’s son Horio Tadaharu similarly succeeded as Castle commander in 1604, then as lord. Tadaharu did not have any male children, so he adopted his half younger brother, Horio Harutaka as his heir. Tadaharu served the Izu Castle’s lord. Horio Harutaka was Tadaharu’s son, born in 1636. Horio Harutomo was Tadaharu’s son, born in 1658, served the lord of Kawagoe Domain, Akimoto Katatomo. Horio Haruyuki was Harutomo’s son. Horio Tadayoshi was Harutomo’s son. He first served the lord of Kawagoe Domain, Akimoto Katatomo, and then became a vassal of the Kuwana Domain. Horio Harurei was Haruyoshi’s adoptive son, his biological father was Hirai Kichidayuu, another vassal of the Kuwana Domain, his biological mother was the second daughter of the Shogunate vassal Hosoi Saichi. Horio Toshichiri was Harurei’s adoptive son, his biological father was Tanaka Budayuu, and his biological mother was a Shogunate vassal Morizumi Tame. Endo Toshisada was Toshichiri’s youngest child, born in 1843, and adopted into the Endo Shounosuke family when he was still small. Endo had two older brothers and three older sisters. His second sister was died a child, and his eldest sister also died early. His two other sisters both married warriors of the Kuwana Domain. As the table shows, then, Endo’s biological father was Horio Naosaemon Toshichiri who came in the tenth generation of the Horio family from Horio Yoshiharu, but was descended biologically from Tanaka Budayuu. So Endo Toshisada’s former family name was Tanaka (3). Endo’s family descent is a typical example of adoption in the Edo period in Japan. 73 （271） Endo Toshisada, Founder of the History of Japanese Mathematics as a New Field of Study: A Defeated Fighter’s Footsteps from the Battle of Ueno in 1868 II. From a Samurai to a Wasan scholar In Japan during the Edo period, it was necessary for every Samurai family to produce male children and to bring them up to become Samurai. Essentially they needed a child to inherit their estate. Well educated Samurai had to be skilled in both literary knowledge and military arts. This kind of education was dispersed at Domain schools or Shogunate schools. But although all male Samurai children intensively studied “Kokugaku” (the traditional Japanese learning), very few of them studied “Wasan” (the traditional Japanese mathematics). Endo was unusual in studying both. 1. Why Endo studied Wasan The birth of Wasan is different from that of the Greek, Indian or Chinese mathematics. Speaking strictly, it started with the importation of mathematics from overseas. The Daigaku-Ryou School was established with the adoption of the ancient style law system (Ritsuryou-sei) in the 7th century Heian period. Several of classics of the Chinese mathematics, along with other works, were imported as textbooks in the discipline of mathematics by way of Korea. But it was not until much later, in the late Muromachi period, that Chinese style abacuses were introduced to Japan. Yoshida Mitsuyoshi adapted the Chinese calculating arts into a Japanese system, published in his work “Jinkouki” in 1627. This was in fact the first technical book of mathematics to be written by Japanese, and it played an important part in awakening an interest and practical understanding of the subject among people at large as well as in setting off a boom in learning mathematics in the form of abacus calculating. By the time Endo was born in late Edo period, Wasan was developed into one of the most refined and sophisticated of Japanese cultural skills. In its developed form, Wasan consisted of the applied art of abacus calculation alongside a more theoretical set of pure mathematical theories. People studied the former as a practical skill, and studied the latter as branch of civilized knowledge like the arts of flower arrangement and the tea ceremony. During the Edo period, professional Wasan scholars were chiefly either abacus teachers at Teragoya schools (supported by temples) , or else manages their own Wasan schools to make their living. Only very few Wasan scholars were Domain school teachers, or employed by the Edo Shounate as astronomers, surveyors, or calendar experts. There were also individual special cases of scholars simply devoting the study of Wasan under the protection of Domain lords who liked Wasan. 74 （272） At the time when Endo was born, there were few male children of the warrior class who studied Wasan, although Wasan was already well established as a systematized dis- cipline.
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