In Mongolian 

Mongolian famous mathematician Myangat (16851770) (almost out of math history) Myangat (16851770) in same period of time Sir Isaac Newton (16431727) 1. Mongol empire (12061691) 2. Mongol Empire or Yuan empire of Hubilai Haan (12591367) in China Manchu Empire (16911911) in Mongolia Manchu Empire (16441911) in China
http://english.people.com.cn/200207/12/eng20020712_99606.shtml CORRECTION: Asteroid Named after Mongolian Scientist An asteroid, numbered 1999AT22, has been named after Myangat (16921765), a Mongolian scientist who lived during the Manchu Dynasty (16441911) in China.
http://www.china.org.cn/english/scitech/36840.htm
In Mongolian Book 1: Mongolian famous mathematician Myangat, Ih erdemten Myangat Ulaanbaatar Mongolia, Academy of Sciences in Mongolian, 238 pages, 1978 · Book 1, p142,
· Book 2: B.Batjargal, Ancient Mongolian mathematics, Ulaanbaatar, Mongolia, in Mongolian, 1976
In English Book 3: B.Szczesniak, Astronomy in old China and Japan, NewYork, 1946 Book 4: Kato Heizaemon, (History of Japanese Mathematics). 2 vols. Tokyo Book 5: Yoshio Mikami, History of Japanese Mathematics
From Chinese resources in English
Book 6: Li Yan, Chinese mathematics (concise history), Oxford, 1987
Minggatu Book 7: JeanClaude, A history of Chinese Mathematics, Springer, 1987
· (Page 9) Kato Heizaemon considers in detail the question of series developments in the work of Minggatu (?1764) · (Page 31) However, as far as the 18^{th} century is concerned, mention should be made by the particularly original works of the astronomer of Mongol abstraction Minggatu (?1764) (known as Ming Antu in Chinese and Myangat in modern Mongolian) on the expansion of circular functions in infinite series. These works, which were unpublished during the author’s lifetime and were first published some 50 years after his death, were the subject of remarkable extensions in the 19^{th} century (expansions in series, trigonometric and logarithmic, apprehended algebraically and inductively without the aid of differential and integral calculus).
· (page 8385) China under the Manchu dynasty (16441911) · The Emperor Kangxi who reigned from 16621722) of Manchu empire in China founded a College of Mathematics in 1713. He asked French Jesuits to teach mathematics. (included Minggatu 28 years old). · In 1723, there were 16 teachers for eight classes of 30 pupils. In 1818, there were only two teachers of Chinese Han ethnic group for 12 Manchu pupils, 6 Mongols, and 6 Chinese. (from book 8, 41p509, 39p485, 48p628). The section disappeared in 1902. Peking university created in 1898 as a result of the Hundred Days of Reform.
· (page 90) Transmission to China of Euclidean geometry and Arabic spherical trigonometry was during Mongol period · (page 93) We must also mention the expansion of the Mongol empire and, more recently, the European penetration into China from the of the 16^{th} century. · (page 101102) Contacts with Islamic countries: Mongol period · There is a ample evidence of the contacts between China and the Islamic countries from the Tang dynasty (618907), but scientific exchanges are generally only thought of as going back to the Mongol period.
·
Instead of massacring the
Muslims, Genghis Khaan wished to use their skills and expertise. He
ordered his troops to spare Muslim craftsmen. Having few artisans among
his own people, Genghis depended upon foreigners, deported a large
number of Muslims from Central Asia to the east. Juvaini notes that
thirty thousand Muslim craftsmen from Samarkand were distributed among
Genghis’s relatives and nobles. Many of these artisans were eventually
settled in Mongolia and or in North China. (book 11, 12)
http://www.mongolinternet.com/JackWeatherford.htm · (page 102) In 1267, a certain Muslim astronomer, called Zhamaluding presented the Mongol Emperor Hubilai Khaan with a perpetual calendar and he was appointed director of the Bureau of Astronomy in Peking, on the orders of Qubilai in 1271. http://user.unifrankfurt.de/~dalen/publicat.htm http://www.orthodoxytoday.org/articles/HuffDialogue2.shtml http://www.admin.ias.edu/hssem/pingyi.html · (p 103) When the Mongols came to power in China, they were interested not only in Islamic astronomy, but also in traditional Chinese astronomy. When the first Ming emperor came to the throne in 1368, (after Mongol empire) he inherited two bureaus of Astronomy, the Chinese and Muslim Bureau.
· (page 143) When the Mongols took Kaifeng in 1233, Li_Zhi (11921279) escaped thanks to the intervention of Yeli Chucai (11901244), a former high ranking Jurchen (Manchu) official who had gone over to serve the Mongols. (book 9, p33) http://wwwgroups.dcs.stand.ac.uk/~history/Mathematicians/Li_Zhi.html · (p143) In 1257, the future Mongol emperor Qubilai sent for Li_Zhi to ask his opinion on how to govern, organize recruitment competitions and interpret earthquakes. (Yuanshi, j160, p 3760). In 1259, he completed his second mathematical work. In 1264, the same Qubilai admitted him to the newly created Hanlin Academy, so that he could participate in the editing of the official dynastic annals of the Liao and Jurchen.
Minggatu · (p163) Collected Essential Principles of Mathematics is a mathematical encyclopedia in 53 chapters. Although the names of the majority of these scholars have not come down to us, we know at least that Minggatu (assistant editor) and Mei Juecheng chief editor). · · (p282) The calculation of Pi (Pi in the Sky by John Barrow) to mark time following a number of spectacular results. Certain mathematicians such as Minggatu (16851770), Xiang Mingda (17891850) used analytical methods of European origin. (Book 8, j 48, 3)
· (p 353355) French Jesuit missionary P.Jartoux (16691720) became famous as an engineer, mathematician and geographer and died in Tartary. He introduced three formulae of infinite series of Sir Isaac Newton (16431727) in 1676 and J.Gregory (16381675) in 1667.
· (p357358) Under these conditions, Chinese research into infinite series form 18^{th} and 19^{th} centures was most probably influenced by European developments, whence the presence of certain European techniques such as addition, subtraction, multiplication and division of series, the reversion of series and the binomial theorem in the works of Minggatu, Dong Youcheng (17911823), Xiang Mingda (17891850) and Dai Xu (18051860). The works of Minggatu are fairly typical in this respect. The Mongol mathematician Minggatu (?1764) expended considerable energy attempting to prove the validity of the above series, it is said that he worked on the question for thirty years. (Book 8, p48) · Contrary to what one might think, Minggatu’s research is not based on hypothetical preexisting Mongol mathematics. (Book 10) · Many traces of this may be found in his mathematical work, including his use of the Euclidean notion of continuous proportion, an algebra of European origin. It is also known that he was involved in the revision of the Compendium of observational and computational astronomy in 1742 and that in 1756 he took part in the topographical survey of the new territories of the West (the present day Xinjiang) which were newly conquered by Qianlong. Finally in 1759, shortly before his death, he became President of the Bureau of Astronomy. http://www.admin.ias.edu/hssem/pingyi.html · On his death Minggatu left an incomplete manuscript. This precious manuscript fell into the hands of his best pupil, Chen Jihin: · In his youth, Master Minggatu, Director of the Bureau of Astronomy learnt mathematics under the aegis of the Emperor Kanghi. He then devoted his whole life to this discipline. When he fell gravely ill, he confided the manuscript (of this work) to his youngest son Jingzhen ans asked me, Jihin, to continue it until it was complete. He said me: “this work entitled “Fast method for obtaining the precise ratio of the division of the circle” contains three procedures for finding, resp.: the length of the circumference as a function of the diameter and the chord and the arrow as a function of the arc. All that comes from writings by French Jesuit missionary P.Jartoux (16691720). Indeed, nothing like it exists in ancient or modern mathematics. I would have liked my colleagues to have been able to use them, unfortunately, Jartoux’s text contains recipes without justifications. Therefore, I did not wish to divulge them, for fear of providing those who might finf them with the Golden needle without secret to the way of using it. I have built up arguments over many years without succeeding in completing the task I gave myself. Thus, I would like my work to be continued.” · I, Chen Jixin, continued this research after the death of my master. When I encountered difficulties I talked about them with Jingzhen and Zhang (was an intendant in the ministry of finance), a student of my master. In 1774, I finally managed to complete the work…
· (page 358) However, the text remained in the manuscript state for a very long time before it was first xylographed in 1839. In 1808, Zhu Hong showed a manuscript copy of the text to Wang Lai (17681813) and Dong Youcheng (17911823). This explains the fact that writings on the subject appeared well before 1839. (H.Kawahara’s reference) Minggatu uses numbers with up to 52 figures to compute.
Book 8: CRZ=Chouren zhuan (Biographies of astronomers and mathematicians) Taipei, 1982
Book 9: Chen Yuan, Western and Central Asians in China under the Mongols, their transformation into China, Monumenta Serica Monographs, Vol 15
Book 10: Shagdarsuren.Ts, 1989, Die mathematische Tradition der Mongolen in W.Heissig and C.C.Mueller eds., Die Mongolen, Innsbruck, PinguinVerlag, pp266267
Book 11: M.Rossabi, 1981, The Muslims in the Early Yuan dynasty, in J.Langlois ed., China under Mongol rule, Princeton, pp257295
Book 12: Needham Joseph. Science and Civilisation in China, vol 3: Mathematics and the Sciences of the Heavens and earth, Cambridge, 1959
Other resources http://aleph0.clarku.edu/~djoyce/mathhist/china.html
· Mongolians owed their achievements in medical science, astronomy and calendar to the influence of the Hans and Tibetans. Mongolian medicine has been best known for its Lamaist therapy, which is most effective for traumatic surgery and the setting of fractured bones. To further develop their medical science, the Mongolians have translated into Mongolian many Han and Tibetan medical works, which include MongolianTibetan Medicine, A Compendium of Medical Science, The of Secret of Pulse Taking, Basic Theories on Medical Science in Four Volumes, Pharmaceutics and Five Canons of Pharmacology. Outstanding contributions have also been made by the Mongolians in the veterinary science. In the field of mathematics and calendar, credit should be given to the Mongolian astronomist and mathematician Ming Antu. During the decades of his service in the Imperial Observatory, he participated in compiling and editing the Origin and Development of Calendar, Sequel to a Study of Universal Phenomena and A Study of the Armillary Sphere. His work Quick Method for Determining Segment Areas and Evaluation of the Ratio of the Circumference of a Circle to Its Diameter (completed by his son and students) is also a contribution to China's development in mathematics. He also made a name for himself in cartography. It was due to his geographical surveys in Xinjiang that the Complete Atlas of the Empire, the first atlas of China drawn with scientific methods, was finished. · http://www.ucl.ac.uk/sts/nk/newtonmoonchina.pdf#search='ming%20antu' · http://www.zrcsazu.si/izrk/Carsologica/Acta322/Pdf322/juznic.pdf#search='ming%20antu' http://saturniancosmology.org/files/china/asrono.txt · In mathematics, Ming Antu, of the Mongolian ethnic group, was a
pioneer in examining the ratio of the circumference of a circle to its diameter in his book /An Express Way to Solve the Ratio of the Circumference of a Circle to Its Diameter/.
http://www.bmcc.cuny.edu/news/RELEASES/2004/040903Fulbright.html · The topics studied by the Fulbright scholars ranged from China’s most ancient (~2000 BC) calculating device, the counting rod, to 17th century Qing dynasty ChineseMongolia mathematician, astronomer and topographer Antu Ming, the first person to measure the entire Chinese territory, the first Chinese mathematician to calculate infinite series, and the first mathematician in the world to formulate Catalan numbers. The group also had the rare opportunity to see counting rods and the abacus used in action by experts, and to see and photograph several important texts that would be unobtainable in the United States.
