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Author - Wang Weiping
Source of the article - Transferred from the WeChat public account Mathematics and Humanities, originally published in the Higher Education Press "Mathematics and Humanities" Series No. 4 "Women and Mathematics"
Who was the first female mathematician recorded in history? General history books believe that hypatia (c. 370–415 AD) was Greek. In fact, as early as more than 300 years before Hypatia, during the Eastern Han Dynasty of China, there was a talented female Ban Zhao who was proficient in astronomy and mathematics, and Mr. Chengru Qiu Chengtong [1] pointed out: "Ban Zhao can be said to be the earliest female mathematician in China. ”
Ban Zhao (c. 49-120 AD), courtesy name Huiban, was a native of Fufeng Anling (present-day Xianyang, Shaanxi Province) in the Eastern Han Dynasty, who was born into a family of eunuchs and scholars of literature and history, and his father Ban Biao, Bogu Tongjin, was a sequel to the "History of History"; the eldest brother Ban Gu, who majored in the Book of Han, was also a generation of famous Confucians; the second brother Ban Chao, who was also known for his deeds of "throwing pens from Rong" and sending envoys to the Western Regions. The Book of the Later Han Dynasty lists the biographies of Ban Zhao and his father and brother, which shows the great learning, influence and contribution of the four members of the Ban family at that time.
Ban Zhao was first and foremost the first female historian on the mainland. This has to start with the "Book of Han" that she sorted out and continued.
Sima Qian's "Records of History" ended in the early years of Emperor Wu of Han, and Ban Biao composed sixty-five articles of "Later Biographies of History" to continue the missing parts of Emperor Wu of Han. After Ban Biao's death, Ban Gu inherited his father's zhi and began to compile the Book of Han on the basis of the "Later Biography of history". After more than twenty years of hard work, Ban Gu completed the main part of the Book of Han. Unexpectedly, in 92 AD, Ban Gu was imprisoned and died because of the defeat of Dou Gendarmes. In this way, the Book of Han, which the Ban father and son spent decades painstakingly compiling, still had the key eight tables and the Astronomical Chronicle not yet completed, and the entire manuscript was in danger of being scattered. At such a juncture, Ban Zhao was ordered by Emperor He of Han (reigned 89-104 AD), put aside his personal grievances, had the great righteousness of the community in mind, and resolutely took up the burden of sorting out and continuing to write the Book of Han. She supplemented the eight tables, and with the assistance of Ma Xu (about 70-141 AD), she wrote the Astronomical Chronicle, and the compilation of the first history of the mainland, the Book of Han, was completed.
The Book of Han contains 800,000 words, mainly describing the history of the 230 years from the first year of Han Gaozu (206 BC) to the fourth year of Wang Mangdi (23 AD). The content covers literature and history, astronomy, calendar, geography, politics, economics, criminal law, etiquette and so on. When it was first formed, it used many ancient characters, and the meaning of the text was difficult, and few people could understand it. Ban Zhao also set up an altar in the East Library Library of the Royal Library to explain the Book of Han. Among those who studied with her at that time was Ma Rong, who later became a scholar, educator, and writer of the Eastern Han Dynasty. The history is recorded as "Ma Rongfu and Your Excellency, to be read by Zhao". Ban Zhao played a crucial role in the dissemination of the Book of Han.
In feudal society, women's history revision has certainly not been done before the twenty-fourth history, and no woman has ever participated in the compilation of history books since then, which can be described as "unprecedented". Later generations have a very high evaluation of the "Book of Han", and there was an allusion to "drinking under the Book of Han". The Song Dynasty poet Su Shunqin (1008-1048 AD), dismissed from his post for the people, retired to Suzhou, built the Canglang Pavilion, gave a copy of the Book of Han, a pot of old wine, and read and drank, drank a cup every time he was comfortable, and sometimes unconsciously drank a bucket. The thirty-seventh time in Jin Yong's "Divine Eagle Heroes" has such a description: "Huang Yaoshi raised a glass of dry wine and sighed: 'The ancients drank with the Book of Han, and the old man today drank with the palm of the little brother (eclipsed soul palm), and the pride was far behind the ancients'. It is also said that this allusion shows the charm of the Book of Han.
Ban Zhao was not only the first outstanding female historian in the history of the mainland, but also a female mathematician, and in fact the first female mathematician in history. We still examine and explain it according to the Book of Han that she participated in compiling.
The status of the Book of Han in the history of Chinese historiography is second only to that of the "History of History" that "the historian's absolute singing, the rhymeless detachment". The book records some historical facts of mathematical significance, which provides valuable information for the study of the history of ancient Chinese mathematics. Among them, the most worth mentioning is that in the "Table of Ancient and Modern People" in the Eight Tables, Ban Zhao arranged the names of 1587 legendary figures and historical figures in a rectangular grid according to the 9 character performance levels set by themselves, essentially using one axis to represent the age and the other axis perpendicular to the character's character. Each character corresponds to a point determined by two numbers (time, character level). In ancient times, more than two thousand years ago, such thinking should be said to be invaluable. Let's take a more concrete look at the method that Ban Zhao created.
The Table of Ancient and Modern People divides people into nine classes. That is, up (9), up (8), up and down (7), up and down (6), middle (5), middle down (4), down (3), down (2), down (1). The higher the number, the higher the level. She only used three Chinese characters "up, down", and after arranging and combining them to get all nine levels. This is also one of the manifestations of The Mathematical Ideas in Ban Zhao's I Ching, which can be promoted and applied. Ban Zhao did not rank the selected characters in order of likes and dislikes, nor was it limited to the emperors and generals, but based on political status, achievements, moral character, contributions, and influence on the time and future generations. Like the upper saints there are Zhou Gong, Kong Qiu, Lao Tzu, etc., the Upper Zhongren people have Nuwa, Gonggong, etc., and there are also 213 Homo sapiens above and below, and they are the lower fools.
Ban Zhao's "Table of Ancient and Modern People" is not without statistical significance. Imagine: if more than fifteen hundred people, in different times and different classes, lay out the life deeds of each person and evaluate them one by one, how big the space is, and how chaotic it is. Ban Zhao first worked the selection of sample points, and the characters must be representative; then he thought hard about the appropriate narrative style, and geniusly took the two factors most related to historical figures, the era and morality, as two axes, and showed the horizontal comparison between different characters and the position of the same character at a glance, which was amazing!
Needless to say, the eight tables of the Book of Han were developed from the "tables" of the Records of History, but the two are very different. Sima Qian used chronology and lunar tables to record historical events, although it can also be seen as having two axes of year and month, in fact, it only reflects the time when the event occurred. Watchmaking requires the overall situation and ingenuity. The works of canonical history have always been difficult to make watches, so they look at the twenty-four histories, and those who have no table have reached fifteen histories.
Ban Zhao not only compiled the Eight Tables, but was also the author of the Book of Han and Astronomical Chronicles. Writing the Astronomical Chronicle is even more difficult. In addition to the need to collect detailed and accurate information, the author is also required to have a rich and solid knowledge of astronomy and mathematics. Ancient Chinese astronomy, calendar and mathematics are closely linked, and Cai Yong believes: "The first rule of the calendar is based on calculation, and astronomy is the test." "If you are not proficient in planning, you must not complete such a huge production as "Astronomical Chronicle". Ban Zhao was proficient in mathematics, which can also be corroborated by the relevant records in the Book of the Later Han Dynasty. "Later Han Shu, Empress Jishang and Empress Dowager Deng": "The empress dowager entered the palace and received scriptures from Cao Everyone, and also astronomy and arithmetic." "Cao Everyone" is Ban Zhao. At that time, people referred to the learned and respected women as "Everyone (reading gu)", and Ban Zhao's husband's surname was Cao, so he was honored as "Cao Everyone". She was commissioned into the palace in the second year of the Han Dynasty (90 AD) and was responsible for teaching the empress and concubines to learn scripture, astronomy, and mathematics.
In the Ban Zhao era, the level of mathematical development was reflected in mathematical texts such as the Nine Chapters of Arithmetic, which had been written at that time. The various algorithms described in the Nine Chapters of Arithmetic were based on mathematical problems handed down before the Qin Dynasty, and were supplemented and revised by the mathematicians of the Han Dynasty according to the needs of the time. According to Liu Hui, Zhang Cang and Geng Shouchang were the main mathematicians involved in the revision. Zhang Cang (c. 250 BC – 152 BC) lived through the Qin and Han dynasties, and was made the Marquis of Beiping in the sixth year of Emperor Gao's reign (201 BC). "Since the Qin Dynasty is the history of the pillar, tomorrow the book will be counted." And make good use of the arithmetic calendar. Geng Shouchang's "counting on goodness and being able to make business and utilitarian profits" was the official of emperor Xuan of Han to the great si nongzhongcheng and was favored by the emperor (see Book of Han and Food Chronicles). As a common mathematical textbook at that time, the Nine Chapters of Arithmetic greatly influenced the development of mathematics in the Two Han Dynasties. The Later Han Shu Ma Yuan Biography has Ma Xu's "BoGuan Qunshu, Good Nine Chapters Arithmetic"; Guangyun Volume IV has records such as "Nine Chapters Technique, Han Xushang, Du Zhi, Wu Chen Chi, Wang Yue and Shan Zhi". In addition, there are also records in the history books of Zheng Xuan, Liu Hong, and others who "passed the nine chapters of arithmetic". It can be seen that this book was an important textbook for intellectuals at that time, including those masters of scripture, to learn mathematics.
The Book of the Later Han Dynasty records mathematics in the Eastern Han Dynasty: "Han Confucianism used mathematical theory to talk about Zhou Yi, and Weishu also talked about astronomical calendar mathematics," so mathematics became part of Confucianism. Yang Xiong imitated the I Ching as the Taixuan Jing, which is actually Yang Xiong's mathematical work. Liu Xin is also a famous mathematician. Eastern Han Confucians studied mathematics more, and Zhang Heng wrote "The Theory of Arithmetic Nets", which coincided with the "Theory of Lingxian" (Zhang Heng's theory of hun tian). Ban Zhao, as a teacher of "Confucianism of the World" such as Ma Rong, is familiar with mathematics and the Nine Chapters, so there is no doubt.
Ban Zhao's family has learned from his father and brother since childhood, and has participated in the compilation of the entire book of the Book of Han. After a long time of study in the Dongguan Library, I was able to see the hundreds of sons. Coupled with the fact that the people who studied under her were proficient in mathematics, we have reason to believe that Ban Zhao was indeed a mathematical master at that time.
bibliography
Yau Chengtong. The Past, Present and Future of Mathematics in China and India. Mathematics and Humanities: Volume 1, 25. Beijing: Higher Education Press, 2010.