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A Brief History of Mathematics in the Ancient and Middle Ages in Korea* 
Three Kingdoms to Goryeo Dynasity 
The official history of Korean Mathematics starts from the Three Kingdoms period (B.C. 57  A.D. 1392). The three kingdoms consist of Goguryeo, Baekje and Silla. The Korean language has its own native numeric words such as Hana (one), Dul (two), On (hundred), Jeumeon (thousand), Dumeon (ten thousand) and so on, and the study of arithmetic had already begun at the beginning of the Three Kingdoms.
The Silla dynasty established a system of arithmetic education based on the example of the Tang Dynasty of China in A.D. 669, right after the unification of the three kingdoms. Silla also adopted the systems of arithmetic education instituted by the other two kingdoms, Goguryeo and Baekje.
The Silla system was founded on the learning centers, each of which was run by arithmetic scholar and an assistant. Students between ages 15 and 30 were educated for 9 years regardless of their status. They were appointed as Daenama (government position at grade 10) upon graduation. The qualifying examinations were based on the mathematical knowledge in the books called Cheolsul, Samgae, Gujang and Yukjang. This system lasted throughout the Goryeo dynasty (A.D. 918A.D. 1392).
Cheolsul was a book listed in the arithmetic education in Tang Dynasty. It is called Zhui Shu in Chinese and translates into The Method of Interpolation. It is thought that the book dealt with sums of infinite series, such as calculating the value of π by using inscribed and circumscribed polygons. Records show that the book was so difficult that a very few wanted to learn it. It is impressive that such a difficult subject, which was renounced in China, had been studied in Korea during Goryeo Dynasty.
Gujang's Chinese title is Jiu Zhang, which translates into The Nine Chapters on the Mathematical Art. It was a fundamental textbook of eastern mathematics and its influence matches that of Euclid's Elements. While western mathematics concentrated on logical deduction depending on the tradition of Euclid's Elements, eastern mathematics was developed with an emphasis on algebra; even geometric problems were solved in an algebraic way. Gujang or Jiu Zhang contains practical problems on measuring rectangular and circular shaped land, proportional distributions, volume of hexahedrons and systems of quadratic equations.
Samgae and Yukjang were not preserved and we do not know their contents.
Geometry and number theory, notably the works of the Greek mathematician Diophantus (A.D. 3C), took precedence over algebra in Greek mathematics. Eastern mathematics, on the other hand, was more advanced in the area of algebra.



Joseon Mathematics 
During the rule of King Sejong of the Joseon dynasty, which came after the Goryeo Dynasty, the arithmetic system was reorganized. This period is known as the golden era of Korean mathematics. According to Sejong Sillok (authentic record of King Sejong), Sanhak Gyojeonso (Office of Arithmetic Publishing) and Seupsanguk (Bureau of Learning Arithmetic) were established and many arithmetic textbooks were published. King Sejong himself learned arithmetic from there. The curriculum consisted of five subjects: Sang Myeong San Beop, Yang Hwi San Beop, San Hak Gye Mong, O Jo San Gyeong and 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 Fa in Chinese, contains problems on magic squares and geometric figures. San Hak Gye Mong, whose Chinese title is Suan Xue Qi Meng, deals with solutions of highorder equations. O Jo San Gyeong, with Chinese title Wu Cao Suan Jing, treats accounts, systems of equations and arithmetic series. The Ji San, titled Di Suan in Chinese, pertains to measurements.
The study of arithmetic, which blossomed during the Sejong era, had been deterred to a great extent by the JoseonJapan war (15921598) and the JoseonQing war (16361637). In particular, a large number of important arithmetic books were lost during the wars. They were restored about a hundred years later during the ruling of King Sukjong (16751720). While Joseon was striving to revive the system of arithmetic education, Japan tried to understand the arithmetic books that they took away from Joseon during the JoseonJapan wars. Japanese arithmetic emerged under the name of Wasan about a hundred years after the war.



Joseon Mathematical Societies 
There were three classes of Joseon’s arithmeticians or mathematicians: the gentry, the illuminists and the bureaucracy. 

(1)

The gentry: Their mathematics, based on the traditional view, was not different from metaphysical ideology. The scholar, Choi SeokJeong (1645 1715), wrote a mathematical book entitled Gu Su Ryak, which could be compared to the theological mathematics of the Roman philosopher Boethius (470524). The Gu Su Ryak emphasizes that the origin of numbers is the first thing to learn and starts with the I Chinglike phrase “Numbers were born from Tao.” His system of numbers like Taiji, Yinyang, Four Realms, etc. is related to I Ching notions.

(2)

The illuminists: The trend of thoughts pursued by the late Joseon scholars is called Silhak, the practical study. The scholars of Silhak evolved the thought of Silsagusi (Seek truth from facts) and led an enlightenment movement. They tended to be encyclopedists and valued mathematics. For example, Hong DaeYong (17311783) built a private astronomical observatory and asserted his own unconventional system of the universe. He discussed mathematics and its links to music, astronomy and calendrical calculation in his book Ju Hae Su Yong.

(3)

The bureaucracy:This middle class was between the gentry and commoners. They were mathematicians in the bureaucratic system. The bureaucrat for arithmetic was called Sansa. He was appointed through a qualifying test and this system of appointment was unique to Joseon. Lists of successful candidates and assessments were recorded in Ju Hak Ip Gyeok An. There were 1627 Sansa between the late 15th century and the late 19th century, all of whom belonged to the families related to the arithmetic bureaucracy, with the exception of 205.



The arithmetic bureaucrat Hong JeongHa wrote Gu Il Jip (Collection of Nine One), which consists of three parts of three volumes entitled Heaven, Earth and Human beingnine volumes in total. According to his book, Hong competed with an arithmetician He GuoZhu in Qing Dynasty. This is the only record of any international competition in Korean history. From this book we also know that Suan Xue Qi Meng was lost and Tian Yuan Shu was dismisssed in China. (Even the book of counting rods disappeared). He GuoZhu was extremely surprised to find that Suan Xue Qi Meng was preserved in Joseon. This finding might have been a stimulus to the Qing Dynasty to reprint the books. Actually Luo ShiLin looked all over for the books and at last found three volumes of Suan Xue Qi Meng, printed in Joseon, at Liu Li Chang in Beijing and reprinted them. It is not known how the books came to Beijing, but he was very excited to have found them. He allegedly said that eastern mathematics could not have been transferred without Joseon.



Way to Modern Mathematics 
During the later part of the last millenium, Joseon tended to exclude I Ching philosophy from traditional mathematics and also ignore mere practical aspects of mathematics. In other words mathematics became a science independent of philosophy, and Joseon mathematics advanced one step from ideological and from practical calculations.
Nam ByeongGil (18201869), a mathematician in the gentry class, wrote a book containing old problems selected from existing books. He conducted research on the mathematical properties rather than practical problemsolving methods. His purpose was to establish a systematic or formal framework of mathematics aside from practical mathematics. He also studied with Yi SangHyeok (1810?), another middle class mathematician, the theory of equations and compared western mathematics with Joseon mathematics. He made conscientious efforts towards modern mathematics. Above all, Yi actively studied werstern mathematics including infinite series through trigonometry.
This shows that he was searching for a way towards modern mathematics. Above all Yi actively studied Western mathematics including infinite series through trigonometry.
Korean mathematics concentrated on the counting rod calculation and Tian Yuan Shu emphasizing the eastern tradition. But the late Joseon era was paving a way towards modern mathematics through independently developed calculations and trigonometry.




A Brief History of Modern Mathematics in Korea 
Period of Establishment (1940’s & 1950’s) 
The Korean Mathematical Society, during the time of its establishment when Korea was under the influence of rapid change, met with many difficulties. One year after Korea gained independence from Japanese rule, the predecessor of the Korean Mathematical Society, known as the Chosun Society of Mathematics and Physics, was established in October, 1946. Yoonshik Choi was elected as the first president of the association, and mathematicians such as Keewon Chang and Chungki Park were teaching mathematics at a college.
At the time of foundation of the First Republic Korean Government in 1948, mathematics teachers at various colleges and schools and those majoring in math were the people who paved the way for Korea's mathematics, and they changed the society's name to the Korean Society of Mathematics and Physics.
On March 11, 1952, two years after the outbreak of the Korean War, the Korean Society of Mathematics and Physics was split into two, thus bringing the Korean Mathematical Society into existence. Three years later, the Society launched its journal, ‘Mathematical Education’, in July.



Period of Transition (1960’s & 1970’s) 
Following the period of the Korean War, the mathematicians who had gone abroad to study received their degrees around 1960. Rimhak Ree, Dock Sang Rim, Kyung Whan Kwun, and ChungNim Lee were among those whose excellent papers were published in major American mathematical journals, while Kapbyung Yoon, Kyunghwan Kwon, Bumshik Chang, Kwangchul Hah, Taeil Seo, and Keesun Song were some of those who returned to the Peninsula and greatly influenced the field of mathematics in Korea.
Following the death of the Society's President Yoonshik Choi in 1960, the Vice President of the Society became the successor President. Due to disbandment of all academic associations through the 516 coup d'etat, the Korean Mathematical Society had its second inauguration on October 9, 1962.
In 1964, the Society began publishing its journal under a new name, 'Math.'. Kyungchan Park was elected as President in 1966, and in the following year the journal 'Math.' was divided into the 'Korean Mathematical Society Journal' and 'Korean Mathematical Society Bulletin' published twice a year.



Period of Major Expansion (19811995) 
In the 1970s, Jungsu Kim and Eullyong Park became consecutive presidents of the Society and the Korean Mathematical Society was registered as a corporation in 1978. Branch societies started publishing their own journals in this period. In 1981, the Korean Mathematical Society joined the IMU and secured its international position for the "Republic of Korea". In 1986, the Society issued its first edition of a collection of papers.
The first Korean Mathematics Olympiad was held in November, 1987, and the Korean Mathematics Olympiad representatives obtained excellent scores in their first participation in the Australian IMO, ranking 22nd out of 60 countries. From the late 1990s, these delegates made it to the top 10 rankings, coming 5th in 2005 and 4th in 2001. In 2000, the 41st IMO was held in Daejeon, Korea. When Jongshik Kim and Mooha Woo became presidents of the Society in the early 1990s, the Korean Mathematical Society laid the groundwork for globalization. At the time when Korea joined the IMU in 1981, Korea was in Group 1. After strenuous efforts by the Society, it was raised to Group 2 in 1993.



Towards Globalization (1996) 
In the late 1990s, ChinKu Chu, Kun Soo Chang, and Sung Ki Kim succeeded to the presidential seat. In October of 1996, "The International Mathematics Convention Commemorating the 50Year Anniversary of KMS" was held, with Rimhak Ree giving a special congratulatory lecture for this special occasion.
The IMU designated the year 2000 as the "World Mathematical Year", and the Korean Mathematical Society followed suit by opening the 41st International Olympiad with the catch phrase "Beginning the new millennium with mathematics". Furthermore, the Society hosted various events to popularize mathematics and opened an international science convention, 'Mathematics in the New Millennium'.
From 2001, Dong Myung Chung, Yong Seung Cho, and then Kyung Chan Min were elected as the Society's President. In January of 2003, the Korean Mathematical Society Journal was registered in the SCIE, bringing much happiness to all members and elevating Korea's mathematical status. In November 2005, every mathematician's dream came true as the National Institute for Mathematical Sciences (NIMS) was founded.
In 2006, 13 agencies were selected by the second BK21, increasing the base for mathematical research and winning a consecutive 3rd place in the 47th IMO. Moreover, greeting its 60th anniversary, the Korean Mathematical Society expanded its global capacity by opening the 'Global KMS Day' academic convention and the "Asia Mathematics Forum".
In 2006, Jeong Han Kim, YongGeun Oh, and JunMuk Hwang gave invited lectures at the 25th ICM held in Madrid. In that year, Korea ranked 12th in the world in terms of SCI publications in mathematics and submitted an application to IMU for its IMU group level to be raised to Group 4. In 2007, IMU raised Korea's group level to Group 4, making Korea the first country whose IMU group level has been raised by two steps at once. With this new confidence, based on a series of highlevel accomplishments, the Korean Mathematical Society has made the hosting of ICM 2014 a prime objective and all members are vigorously applying their energy to ensure that the Society will continue to be fully recognized and acknowledged in the international world.






* An Article from the KIAS Newsletter 2009 (Title: History of Mathematics in Korea)
Written by YongWoon Kim, Hanyang University
Translated by PooSung Park, Kyungnam University 








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