Mathematics in the Ancient and Middle Ages of Korea

Home , Hong (Korean surname), Silhak, Silla

History of Mathematics & Astronomy in Korea

two kingdoms, Goguryeo and Baekje. Joseon-Japan war (1592-1598) and the Joseon-Qing war (1636-1637). In particular, a large number of Newsletter important arithmetic books were lost. They were retrieved about a hundred years later during the rule of The Silla system was based on learning centers, each equipped with an King Sukjong (1675-1720). While Joseon was striving to revive the system of arithmetic education, Japan arithmetic scholar and an assistant. Students were aged between 15 and tried to understand the arithmetic books that they took away from Joseon during the wars. Japanese 30, irrespective of their status and they were educated for 9 years. They arithmetic emerged in the name of Wasan about a hundred years after the wars. History of Mathematics & Astronomy in Korea were appointed as Daenama (10th grade government position) after Kowa Seki, the originator of Wasan, started studying arithmetic by transcribing Joseon’ s books and he graduation. The qualifyingCheolsul examinations, Samgae, Gujangwere basedand Yukjangon knowledge. This system of invented a symbolic algebra, which describes counting rods used in the lastedbooks untilcalled the Goryeo dynasty (A.D. 918-A.D. 1392). Tian Yuan Shuof San Hak Gye Mong (Suan Xue Qi Meng) as drawings. Tian Yuan Shuwas the method of solving high degree polynomials and Cheolsulwas a book listed in the Tang dynasty's arithmetic education. It was the most outstanding achievement of Eastern mathematics. The same method was published as is called Zhui Shu in Chinese and translates toThe Method of approximate solutions of high degree polynomials many centuries later in the 19th century by Homer, Interpolation . It is thought that the book dealt with the calculation of a British mathematician. sums of infinite series, like calculating value of pi, by using inscribed and circumscribed polygons. But the book did not survive till the Joseon Mathematical Societies present. It has been recorded that the book was so difficult that few [ The Nine Chapters on the There were three classes of Joseon’s arithmeticians or mathematicians: the gentry, the illuminists and the wanted to learn it. It is impressive that such a difficult subject that was Mathematical Art ] bureaucracy. forgotten in China was being studied in Korea during the Goryeo dynasty period. (1) The gentry: their mathematics, based on the traditional view, was not Gujang's Chinese title is Jiu Zhangwhich translates to The Nine Chapters on the Mathematical Art. It was different from metaphysical ideology. The scholar, Seok-Jeong Choi (1645- a fundamental textbook of Eastern mathematics and its influence matches that of Euclid's Elements. While 1715), wrote a mathematical book calledGu Su Ryak, which could be Western mathematics concentrated on logical deduction depending on the tradition of Euclid's Elements, compared to the theological mathematics of the Roman philosopher Eastern mathematics developed focusing on algebra and so it solved even geometric problems in an Boethius (470-524). The Gu Su Ryakemphasizes that the origin of numbers algebraic way. Gujang or Jiu Zhang contains practical problems about measuring rectangular and circular is the first thing to learn and starts with the I Ching-like phrase “Numbers shaped land, proportional distributions, volume of hexahedrons and systems of quadratic equations. were born from Tao.” His system of numbers like Taiji, Yin-yang, Four Realms, etc. is related to I Chingnotions. Samgaeand Yukjangwere, however, not preserved and so we do not know their contents. (2) The illuminists: the trend of thought pursued by the late Joseon scholars In the areas of geometry and number theory Greek mathematics takes precedence, notably the works of is called Silhak, the practical study. The scholars ofSilhak evolved the the Greek mathematician Diophantus (A.D. 3C), but Eastern mathematics was more advanced in the thought of Sil-sa-gu-si (Seek truth from facts) and led an enlightenment area of algebra. [ Seok-Jeong Choi's Gu Su Ryak] movement. They tended to be encyclopedists and valued mathematics. For

46 Korea Institute for Advanced Study 47 History of Mathematics & Astronomy in Korea

Mathematics in the Ancient and Joseon and Japanese Mathematics During the rule of King Sejong of the Joseon dynasty which came after the Goryeo dynasty, the arithmetic Middle Ages of Korea system was reorganized. This period is known as the golden age of Korean mathematics. According to Sejong Sillok(authentic record of King Sejong), Sanhak Gyojeonso(Office of Arithmetic Publishing) and Yong-Woon Kim, Hanyang University Seupsanguk (Bureau of Learning Arithmetic) were established and many arithmetic textbooks were Translated by Poo-Sung Park, KIAS published. King Sejong himself learned arithmetic here. The curriculum was composed of five subjects: Sang Myeong San Beop, Yang Hwi San Beop, San Hak Gye Mong, O Jo San Gyeongand Ji San. The first, Sang Myeong San Beop, whose Chinese title is Xiang Ming Suan Fa, explains the elements of metrology, acoustics and computation of series. Yang Hwi San Beop, or Yang Hui Suan Fain Chinese, The official history of Korean Mathematics starts from the Three Kingdoms period (1C B.C. - A.D. 10C). contains problems about magic squares and geometric figures. San Hak Gye Mong, whose Chinese title is The three kingdoms consist of Goguryeo, Baekje and Silla. The Korean language has its own native numeric Suan Xue Qi Meng, deals with solutions of high degree equations.O Jo San Gyeong, with Chinese title words such as Hana (one), Dul (two), On (hundred), Jeumeon (thousand), Dumeon (ten thousand) and so on Wu Cao Suan Jing, treats accounts, systems of equations and arithmetic series.Ji San, titled Di Suan in and arithmetic was already being studied from the beginning of the Three Kingdoms period. Chinese, is about measurements. The Silla dynasty established a system of arithmetic education based on that of the Tang dynasty of China in A.D. 669, right after the unification of the three kingdoms and then absorbed the systems of the other The study of arithmetic which blossomed during the Sejong era was damaged to a great extent by the KIAS two kingdoms, Goguryeo and Baekje. Joseon-Japan war (1592-1598) and the Joseon-Qing war (1636-1637). In particular, a large number of Newsletter important arithmetic books were lost. They were retrieved about a hundred years later during the rule of The Silla system was based on learning centers, each equipped with an King Sukjong (1675-1720). While Joseon was striving to revive the system of arithmetic education, Japan arithmetic scholar and an assistant. Students were aged between 15 and tried to understand the arithmetic books that they took away from Joseon during the wars. Japanese 30, irrespective of their status and they were educated for 9 years. They arithmetic emerged in the name of Wasan about a hundred years after the wars. History of Mathematics & Astronomy in Korea were appointed as Daenama (10th grade government position) after Kowa Seki, the originator of Wasan, started studying arithmetic by transcribing Joseon’ s books and he graduation. The qualifyingCheolsul examinations, Samgae, Gujangwere basedand Yukjangon knowledge. This system of invented a symbolic algebra, which describes counting rods used in the lastedbooks untilcalled the Goryeo dynasty (A.D. 918-A.D. 1392). Tian Yuan Shuof San Hak Gye Mong (Suan Xue Qi Meng) as drawings. Tian Yuan Shuwas the method of solving high degree polynomials and Cheolsulwas a book listed in the Tang dynasty's arithmetic education. It was the most outstanding achievement of Eastern mathematics. The same method was published as is called Zhui Shu in Chinese and translates toThe Method of approximate solutions of high degree polynomials many centuries later in the 19th century by Homer, Interpolation . It is thought that the book dealt with the calculation of a British mathematician. sums of infinite series, like calculating value of pi, by using inscribed and circumscribed polygons. But the book did not survive till the Joseon Mathematical Societies present. It has been recorded that the book was so difficult that few [ The Nine Chapters on the There were three classes of Joseon’s arithmeticians or mathematicians: the gentry, the illuminists and the wanted to learn it. It is impressive that such a difficult subject that was Mathematical Art ] bureaucracy. forgotten in China was being studied in Korea during the Goryeo dynasty period. (1) The gentry: their mathematics, based on the traditional view, was not Gujang's Chinese title is Jiu Zhangwhich translates to The Nine Chapters on the Mathematical Art. It was different from metaphysical ideology. The scholar, Seok-Jeong Choi (1645- a fundamental textbook of Eastern mathematics and its influence matches that of Euclid's Elements. While 1715), wrote a mathematical book calledGu Su Ryak, which could be Western mathematics concentrated on logical deduction depending on the tradition of Euclid's Elements, compared to the theological mathematics of the Roman philosopher Eastern mathematics developed focusing on algebra and so it solved even geometric problems in an Boethius (470-524). The Gu Su Ryakemphasizes that the origin of numbers algebraic way. Gujang or Jiu Zhang contains practical problems about measuring rectangular and circular is the first thing to learn and starts with the I Ching-like phrase “Numbers shaped land, proportional distributions, volume of hexahedrons and systems of quadratic equations. were born from Tao.” His system of numbers like Taiji, Yin-yang, Four Realms, etc. is related to I Chingnotions. Samgaeand Yukjangwere, however, not preserved and so we do not know their contents. (2) The illuminists: the trend of thought pursued by the late Joseon scholars In the areas of geometry and number theory Greek mathematics takes precedence, notably the works of is called Silhak, the practical study. The scholars ofSilhak evolved the the Greek mathematician Diophantus (A.D. 3C), but Eastern mathematics was more advanced in the thought of Sil-sa-gu-si (Seek truth from facts) and led an enlightenment area of algebra. [ Seok-Jeong Choi's Gu Su Ryak] movement. They tended to be encyclopedists and valued mathematics. For

46 Korea Institute for Advanced Study 47 History of Mathematics & Astronomy in Korea

example, Dae-Yong Hong (1731-1783) built a private astronomical observatory and asserted his own unconventional system of the universe. He discussed mathematics and its links to music, astronomy and Traditional Korean Astronomy : calendrical calculation in his bookJu Hak Su Yong. Besides, he separated mathematics from philosophy and introduced the concept of infinity through the calculation of pi. Science of the Heavens

(3) The bureaucracy: this middle class was between the gentry and commoners. They were Changbom Park mathematicians in the bureaucratic system. The bureaucrat for arithmetic was called San-sa. He was School of Physics, KIAS appointed through a qualifying test and this system of appointment was unique to Joseon. The lists of Astronomy begins with observing the heavens. After constant and meticulous observation, people successful candidates and assessments were recorded in Ju Hak Ip Gyeok An. There were 1627 San-sa named the heavenly bodies, connected the stars to form constellations, and made constellation between the late 15th century and the late 19th century who all belonged to families related to the charts, which are maps of the heavens. It was only after a lot of observational data had been arithmetic bureaucracy , with the exception of 205 of them. collected that information about the heavenly bodies could be systemized and regularity found in astronomical phenomena, ultimately leading to the invention of cosmology to explain the universe The arithmetic bureaucrat Jeong-Ha Hong wrote Gu Il Jip (Collection of Nine One), which is composed of and its changes. Based on their understanding of the universe and the principles of its motion, nine volumes in total and has three parts of three volumes each, entitled Heaven, Earth and Human being. According to his book, Hong competed with a Qing dynasty arithmetician Guo-Zhu He. This is the only people could then formulate accurate calendars with a view to predicting future astronomical

record of any international competition in Korean history. From this book we also know that Suan Xue Qi phenomena. Hence, an introduction to traditional Korean astronomy should reflect the generic KIAS aspects of the science and begin with an examination of the astronomical observations made by

Meng was lost and Tian Yuan Shuwas forgotten in China. (Even counting rods disappeared). Guo-Zhu He Newsletter was extremely surprised to find that Suan Xue Qi Mengsurvived in Joseon. This find might have been a ancient Koreans. stimulus to the Qing dynasty. Shi-Lin Luo found three volumes of Suan Xue Qi Meng, printed by Joseon, Of the three developmental phases of astronomy- accumulating observational information, in Liu Li Chang at Beijing and reprinted them. It was not known how the books came to be in Beijing, but systematizing astronomical knowledge, and then creating a model of the universe and forecasting History of Mathematics & Astronomy in Korea he was very excited on finding them. He said that Eastern mathematics could not have been handed down astronomical phenomena -traditional Korean astronomy had brilliant achievements in the first two. without Joseon. Ancient Korean kingdoms established their own bureaus of astronomy, built observatories, and employed officials dedicated to observing astronomical phenomena. Official observations of Way to Modern Mathematics astronomical phenomena started from the 1st century B.C. and the extensive records handed down Although it was a somewhat later part of the last millenium, Joseon had a tendency to excludeI Ching include over 20,000 items. Comparably detailed records were made only by Korea’s immediate philosophy from traditional mathematics and also ignore the mere practical aspects. In other words neighbors: China, which began official recording of astronomical phenomena about 2,800 years mathematics was thought of as an independent part of science, so it was not within the purview of ago (circa 8th century B.C.); and Japan, ideological or practical mathematics. Byeong-Gil Nam (1820-1869), a mathematician in the gentry class, wrote a book containing old problems which began 1,400 years ago (7th century selected from existing books. He researched their mathematical properties rather than practical problem A.D.). solving methods. His purpose was to establish a systematic or formal framework of mathematics away Ancient Koreans developed a systematic from mere practical mathematics. He also studied with Sang-Hyeok Yi (1810-?), another middle class understanding about the kinds of heavenly mathematician, the theory of equations and compared Western mathematics with Joseon mathematics. bodies and their motions by observing, This shows that he was searching for a way towards modern mathematics. Above all Yi actively studied over a long period, the sun and the moon, Western mathematics including infinite series through trigonometry. the five visible planets (Mercury, Venus, Korean mathematics concentrated on the counting rod calculation andTian Yuan Shu emphasizing the Mars, Jupiter and Saturn), and numerous Eastern tradition. But the late Joseon was paving the way towards modern mathematics through [A dolmen in Korea with cupmarks on the southern side] stars. Of the astronomical knowledge independently developed calculations and trigonometry. gathered in ancient times, that which can be confirmed is the identification of constellations and astronomical directions. The origin of Korean astronomy dates back to the prehistoric Stone and Bronze Ages. Korea is a land of dolmens. Dolmens found concentrated in the territory of ancient Korean kingdoms, as well as stone chamber tombs and burial items therein, are representative scientific relics that show the application of astronomical observations to real life. Astronomical knowledge from prehistoric times not only had a decisive influence on the development of astronomy in the three kingdoms (Goguryeo, Baekje and Silla) after the 1st century

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