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 mathematics), 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 traditional 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 century. 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 discipline. In general, it was still much more important for sons of warrior families to study Chinese classics and military arts than Wasan. Of course, Endo was also expected to grow up into a Samurai in much the same way as the children around him. That seemed to be the path that was prepared for him in the future. If Endo studied Wasan, it was because he acquired a taste for it as part of his general all-round education. As noted by Mikami Yoshio (Mikami: “A Brief Biography of Endo Toshisada”, 1961), Endo never thought to raise himself in the world using Wasan.

2. How Endo studied Wasan

The educational system in the late Edo period consisted of the Shogunate schools, Domain schools, and private schools (4). The Shogunate schools were located in Edo for the Shogunate vassal, the Shoheiza- ka-gakumonjo was the highest level institution. Domain schools ﬁrst appeared in the 1660s for the education of male children of the Samurai warrior class. The curriculum originally consisted of Chinese literary classics “the Four Books” and “the Five Classics”, and military arts. But this began to change from the middle of the Edo period. Some Domain schools added natural sciences to the curriculum, included Wasan although it was by no means a core subject. Domain schools were usually in the places where the Domain itself was located, but most large most Domains established one in their Domain Residences in Edo for their warrior families who always lived there. The Kuwana Domain set up a Domain school in its Domain Residence in Hacchoubori, Edo, and named it Rikkyou-kan (5). Male children usually entered Domain schools at 7 or 8 years old and left sometime the ages of 14 and 20 (6). Endo first learned the basics of abacus calculating from his family, and then, after mastering the foundations of Wasan at the Rikkyou-kan Domain School, went to study it at a more advanced level under Hosoi Wakasa.

(1) Endo’s early education in his family Endo came from a very cultured family. When it came to education, his parents looked beyond the basic Samurai upbringing and attached greater importance to the general culture, including Wasan, which was certainly not needed to be Samurai. The study of Wasan began with the mastery of the abacus. At the outset, his mother

75 （273） 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 taught him “you can understand the law of the universe by yourself with the art of the abacus, so you should not slight the abacus.” His father and his older brothers taught him to read Chinese classics as well as arithmetical skills on the abacus. When he was six years old, they introduced him to the “Great learning”, the starting part of the Chinese “the Four Classics”, and then when he was nine, his father taught him arithmetic and the division table for use with abacus.

(2) The second course of study at the Domain school When he was nine, he was admitted to the Rikkyou-kan Domain School, where he began receiving the standard the education for becoming a Samurai. But in addition to the usual literary and military arts courses, he also continued with arithmetic. He did his best to keep his arithmetical studies secret because it was considered a shame in the Domain schools to pursue studies of that sort. Actually, very few students took arithmetic at that time.

(3) The third stage, studying under the private tuition of Hosoi Wakasa In around the 1866, Endo began systematically studying Wasan from Hosoi Wakasa. Hosoi was an outstanding disciple of Wada Nei, was one of the most famous traditional Japanese mathematicians of the late Shogunate time. Under him, Endo studied everything from “Tianyuan-shu” (the Chinese traditional algebra), “Tenzan-jutsu” (the traditional Japanese algebra) to “Enri” (the Japanese style calculus).

III. From a Wasan scholar to a Yozan scholar

The Tokugawa Shogunate was the longest period of unbroken rule in Japanese feudal history. Under the isolation policy from 1639 to 1853, Japan grew gradually weaker against the western powers in both diplomatic and military terms, while Japanese culture, including Wasan, thrived and bared important fruits. That might have been one of the main reasons why the more cultured vassal classes in the Shogunate and Domain terri- tories came to favor modernization and westernization, and eventually backed the Meiji Restoration. The average Samurai classes were less favorably inclined toward this kind of thinking, even in cases where they did not actively oppose it, because for them the revo- lution might easily mean losing their estate, ruler, everything. This is why there was so much armed resistance to the new government during the restoration. The more scholarly members of the Samurai class were often pulled two ways. As

76 （274） scholars, they might favor charge because they had understood that Western science and technology were necessary to make Japan more powerful through the Dutch studies, but as Samurai belonged with the Shogunate, and their feeling were the same as those of the average Samurai, so they tended to join the forces of resistance as soon as a battle occurred. Endo was a mathematician, but nevertheless engaged in the Battle of Ueno as an anti-government “Shogitai” ﬁghter in 1868. After escaping from the battle, he gave up the study of Wasan, began studying the Western mathematics, and eventually became a teacher at the Tokyo Normal School ( the predecessor of Tsukuba University).

1. Engaging in the Battle of Ueno

The Battle of Ueno, an episode of the Boshin Civil War, was fought on July 4, 1868 between the Meiji government forces and so-called “Shogitai”volunteer force. The name “Shogitai” means the “League to Demonstrate Righteousness”, it was established on Feb.21, 1868, for the purpose of guarding Edo and protecting the 15th Tokugawa Shogun Yoshinobu who had been confined in the Ueno Kanei Temple. Shogitai fighters consisted of the loyalists of the Tokugawa Shogunate and other people who resisted the new government. The battle finished with the defeat of Shogitai, Over 200 Shogitai fighters died, but Endo was one of the ones who succeeded in escaping from Edo.

2. Returning to mathematical studies in his years of confinement

After the battle of Ueno, Endo initially escaped from Edo and went into hiding the new government authorities for several months. Then he returned to Edo, and made a living for about half a year carrying goods under a false name. He returned to the Kuwana Domain on August 28, 1869 with another 2 defeated Shogitai fighters. All three of them used false names. He was conﬁned in Kuwana. Endo restarted to his mathematical studies during the time. In 1869, He became a Wasan teacher at the Domain school in the Domain territory of Kuwana.

3. from Wasan teacher to Yozan teacher

In 1872, The new Meiji government reformed the education system, making the new

77 （275） 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 education system public. Wasan as a subject was to be totally abolished, and Yozan (the Western mathematics) adopted in its place. Accordingly, Endo decided to switch to Western mathematics. Endo and two other friends left Kuwana on February 18th, in 1872 and arrived in Tokyo on February 26th. In Tokyo, Endo worked to support himself while attending the Yozan school, initially learning with very much younger in age than himself. The study began from the basics of addition, subtraction, multiplication and division. Endo was able to master Western mathematical knowledge from the basics up to calculus in a few months thanks to his previous knowledge of Wasan. He became a Yozan teacher in August of the same year. From that point on, he began to teach Western mathematics at the Tokyo Normal School and other places, and published several textbooks on the Western mathematics.

IV. From a mathematician to a historian of mathematics

Tokyo Sugaku Kaisha (The Tokyo Society of Mathematics, the predecessor of the present-day mathematical Society of Japan) was established in 1877, and Endo Toshisada became a member. The society consisted of Yozanka (the Western mathematicians) and Wasanka (the traditional Japanese mathematicians). These two groups often stood in opposition, but the former was stronger than the latter and usually in controlling position. Endo began to realize that there was a need to make the history of Wasan clear, and to pass down the knowledge of past men of learning as a legacy to coming generations. It would soon be forgotten if he didn’t do something about recovering and transmitting it now. In 1878, Endo started his research into the history of Wasan. In 1886, it was finally beginning to take historical shape and in February of that year he gave a lecture on the history of Wasan at the Great Japan Society of Education, which it was subsequently published in Issues No.40 and No.41 of the society’s Journal. Endo went on expanding on this first overview of the field, and in May 1893, his fuller account was completed. On May 16th, he delivered a grand summary of his research results at the plenary session of the Great Japan Society of Education, and then the summary was published on the Journal of the society No.100. On November 1896, “A History of the Mathematics of great Japan” was formally published as a book style by the Mitsui Zaibatsu’s aid in the costs of publishing.

78 （276） Conclusion

Endo Toshisada started working on the history of Wasan in 1878, completed it in 1893, and published it in 1896, it took him eighteen years. Endo Did not grew up in the world with mathematics when he was small, but he eventually devoted his life to mathematical education and the study of mathematical history. Above all, he pioneered in the field of the East Asian history of mathematics by founding the history of Japanese mathematics as a new field of study, leaving us with a precious legacy today. On April 20th, 1915, Endo died of stomach cancer. He was 73 years old. The Japan government awarded him “the Sixth Class Zuihousho Prize” for commending his achieve- ments in the study of history Japanese mathematics. Today, Endo Toshisada’s work “A history of Mathematics of Great Japan” has been an existence like the Bible in the field of the East Asian history of mathematics.

Reference books and papers (1) This paper primarily follows books and papers as follows ① Endo Toshisada, A History of Mathematics of Great Japan, (Kouin Shinshi Sha, Tokyo, 1896) ② Endo Toshisada, edited by Mikami Yoshio, The Expanded History of Japanese Mathematics, (Kousei Sha, Tokyo, 1918) ③ Endo Toshisada, edited by Mikami Yoshio, edited and corrected by Hirayama Akira, The Expanded History of Japanese Mathematics, (Kousei Sha Kousei Kaku, Tokyo, 1981) ④ Mikaki Yoshio’s paper, “A Brief Biography of Endo Toshisada” (1961), Endo Toshisada, edited by Mikami Yoshio, edited and corrected by Hirayama Akira, The Expande History of Japanese Mathematics ( Kousei Sha Kousei Kaku, Tokyo, 1981) Mikami’s this paper primarily followed Endo Toshisada’s own handwriting autobiography “A record of going to Tokyo” (unpublished). Endo’s this manuscript is possessed by The Tohoku University now, has not been opened yet for the public. (2) See (1)- ③ , pp.655-656. “Dictionary of History Dictionary” ( Shougakukan, 2000, 2007) (3) See(1)- ③ , P.655. (4) Ministry of Education, Culture, Sports, Science and Technology Japan: “Education of the late shogunate”, http://mext.go.jp/b-menu/hakosho/html/others/detail/1317577.htm. (5) Tanaka Katsuyoshi: ‘A Study of Schools in Feudal Lords’ estates’, Keio Associated Repository of Academic Resources. Inagaki Tahiko: ‘The Contents and methods of Learning in the Domain schools”, The Faculty of Literature, The Teikyou University Journal 27, ( 2002) (6) See(5)-2,p.1.

79 （277） 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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