Blaschke, Osgood, Wiener, Hadamard and the Early Development of Modern Mathematics in China
aa r X i v : . [ m a t h . HO ] S e p Blaschke, Osgood, Wiener, Hadamard and the EarlyDevelopment of Modern Mathematics in China
Chuanming Zong
Abstract.
In ancient times, China made great contributions to world civi-lization and in particular to mathematics. However, modern sciences includ-ing mathematics came to China rather too late. The first Chinese universitywas founded in 1895. The first mathematics department in China was for-mally opened at the university only in 1913. At the beginning of the twenti-eth century, some Chinese went to Europe, the United States of America andJapan for higher education in modern mathematics and returned to Chinaas the pioneer generation. They created mathematics departments at theChinese universities and sowed the seeds of modern mathematics in China.In 1930s, when a dozen of Chinese universities already had mathematicsdepartments, several leading mathematicians from Europe and USA visitedChina, including Wilhelm Blaschke, George D. Birkhoff, William F. Osgood,Norbert Wiener and Jacques Hadamard. Their visits not only had profoundimpact on the mathematical development in China, but also became socialevents sometimes. This paper tells the history of their visits.2020 Mathematics Subject Classification: 01A25, 01A60.
1. Introduction and Background
In 1895, Peiyang University was founded in Tianjin as a result of the westernizationmovement. In 1898, Peking University was founded in Beijing. They are the earliestuniversities in China.On May 28, 1900, Britain, USA, France, Germany, Russia, Japan, Italy and Austriainvaded China to suppress the Boxer Rebellion which was an organized movementagainst foreign missionaries and their followers. On August 14, 1900, more than 20,000soldiers of the allied force occupied the Chinese capital Beijing and the emperor’s familywith some high ranking officials and servants escaped to Xi’an. On August 8, 1901, whenthe Qing government agreed all the requirements of the eight nations including payingthem huge indemnity (the Boxer Indemnity), the allied force withdrew from Beijing.On December 28, 1908, after four years of hard diplomatic negotiation, Americangovernment finally admitted that the indemnity was overpaid and decided to return theoverpayment of the Boxer Indemnity to China. That was 11.96 million US dollars. Both At the end of the nineteenth century, after the second Anglo-Chinese war, foreign missionaries wereunder particular protection in China. Gradually, their followers also benefited from the protection. In1897, there was a conflict between the followers of a church and the local villagers in Shandong Province.When the villagers thought that they were treated unfairly, they asked a famous boxer Sanduo Zhao toadminister justice. They got the expected justice! Afterwards, organized boxer gangs for the purpose offighting with the missionaries and their followers were quickly formed and spread from Shandong to theneighbor provinces, finally to Tianjin and Beijing. Many churches were destroyed and more than 100,000people from both sides were killed. At that time, Empress Dowager Ci Xi (1835-1908) was in power.Since the rebels took a slogan supporting the Qing rulers and opposing foreign powers , they obtainedtacit permission from Ci Xi. In June 1900, more than 100,000 boxer rebels gathered in Beijing. Whenthousands of missionaries and their followers fled to the foreign embassies, the boxer rebels sieged theembassy area in Beijing. sides agreed to set up an education foundation with this money to support Chinesestudents to study in America. According to the agreement, in the first four years from1909, China could send one hundred students each year and thereafter fifty students ayear until the fund was exhausted. Meanwhile, Tsinghua School was founded in 1909 totake charge of the selection and preparation of the students.The education foundation set up by the returned Boxer Indemnity was crucial forthe Chinese modern mathematics. It led to the first Chinese Ph.D Mingfu Hu (1891-1927) in Harvard in 1917, educated the first generation of the great Chinese mathemat-ical educators such as Li-Fu Chiang (Chan-Chan Tsoo, 1890-1978) and King-Lai Hiong(1893-1969), and educated the first generation of globally known Chinese mathemati-cians such as Loo-Keng Hua (1910-1985), Shiing-Shen Chern (1911-2004) and Pao LuHs¨u (1910-1970).In 1912, the first mathematical department in China was set up at Peking Universitywith two professors: Zuxun Feng (1880-1940) and Junji Hu (1886-??). The next yearit enrolled two students as a start. Professor Feng taught analytical courses such ascalculus, function theory and differential equations, and professor Hu taught the otherssuch as Euclidean geometry and integer theory.Zuxun Feng enrolled in Peking University as a undergraduate student in 1902. Twoyears later, he was chosen to study mathematics in Japan supported by Peking Univer-sity. He graduated from Kyoto Imperial University in 1909, specialized in differentialequations. This made him the first Chinese who ever had a complete university edu-cation in mathematics. Junji Hu went to Japan in 1903 with his brother. He studiedMining Metallurgy and graduated from Tokyo Imperial University. At that time, helearnt some modern mathematics. In particular, when he took the teaching positionat Peking University, he visited Tokyo Imperial University once again to improve hismathematics.In 1917, two more professors joined the mathematical faculty: Fen Qin (1887-1973)and Renfu Wang (1886-1959). Qin obtained a Master degree in astronomy in 1909 andWang obtained a Bachelor degree in mathematics in 1913, both from Harvard. At thattime, the math department had seven faculty members and more than twenty students.It offered a dozen of mathematical courses such as Euclidean geometry, calculus, functiontheory, differential equations, harmonic functions, theoretic physics, abstract algebra,modern geometry, group theory and number theory.In 1919, Nankai University was founded in Tianjin, China. The next year it set upa mathematical department and appointed Li-Fu Chiang, who obtained his Ph.D fromHarvard under the supervision of J. L. Goolidge, as the chair professor. It was thesecond mathematical department in China. In fact he was the only faculty memberof the math department for four years. He alone taught various courses in analysis,geometry and algebra. During that hard time, he educated several promising studentssuch as Chin-Nien Liu (1904-1968), Tsai-Han Kiang (1902-1994) and Yu-Cheng Shen(1901-1978). Afterwards, all Liu, Kiang and Shen obtained their Ph.D from Harvardand made distinguished contribution to modern mathematical development in China.In 1920, National Southeast University was founded in Nanjing, China. In the nextyear it set up a mathematical department and appointed King-Lai Hiong (1893-1969),who obtained a Master degree from Universit´e de Montpellier in 1919, as its foundingchair professor. He designed the courses, prepared lecture notes and taught analyticgeometry, spherical geometry, calculus, analytic functions, differential geometry anddifferential equations. In 1922, Zi-Xie Duan (1890-1969) joined the mathematical facultyas a professor. Then the department could offer more mathematical courses. Duan wentto France in 1913. He obtained a Master degree in mathematics from Lyon in 1920. In 1927, Tsinghua University set up a mathematical department. King-Lai Hiong andZhi-Fan Zheng (1887-1963) were appointed as the first two professors, with professorZheng as chairman. Zhi-Fan Zheng studied mathematics at Cornell and graduated in1910. Afterwards, he visited Harvard to improve his mathematics for one year.In three years, two more professors joined the faculty: Dan Sun (Guang-Yuan Sun,1900-1979) and Ko-Chuen Yang (1896-1973). Both Dan Sun and Ko-Chuen Yang ob-tained their Ph.D from Chicago in 1928, the first wrote a thesis in differential geometryunder the supervision of E. P. Lane and the second wrote his thesis in number theoryunder the supervision of L. E. Dickson. Then, the mathematical faculty at Tsinghuabecame one of the strongest math faculties in China.In 1930s, China had already more than forty universities and several competitivemathematical departments such as the departments at Peking University, TsinghuaUniversity, Zhejiang University, Central University, Nankai University, Chiao Tung Uni-versity, Kwang Hua University and Wuhan University (see Zhang [10]). Up to 1930,eighteen Chinese obtained their Ph.D in mathematics, as listed in the following table.They played crucial roles for introducing modern mathematics to China (see Zhang [11]).Name University Time FieldMingfu Tah Hu Harvard 1917 AnalysisChan-Chan Tsoo Harvard 1919 GeometryJung Sun Syracuse 1921 AlgebraDavid Yule Harvard 1922 Mathematical LogicBing-Chin Wong UC Berkeley 1922 GeometryShih-Luan Wei G¨ottingen 1925 AnalysisZhao-An Zeng Columbia 1925 GeometryKun-Ching Chu G¨ottingen 1927 AnalysisKo-Chuen Yang Chicago 1928 Number TheoryDan Sun Chicago 1928 GeometryChin-Yi Chao Lyon 1928 AnalysisWei-Kwok Fan Lyon 1929 AnalysisKien-Kwong Chen Tohoku 1929 AnalysisTsun-Shien Lian Lyon 1930 AnalysisTsai-Han Kiang Harvard 1930 TopologyChin-Nien Liu Harvard 1930 AnalysisHung-Chi Chang Michigan 1930 PDEShu-Ting Liu Michigan 1930 AnalysisIn 1918, Dr. Mingfu Tah Hu published his thesis at
Transactions of the AmericanMathematical Society . It was the first mathematical research paper published by Chinese.Up to 1930, about one hundred mathematical papers were published by Chinese authors.
2. Painlev ´ e and Russell’s Visits to China The first western mathematicians to visit China were Paul Painlev´e (1863-1933) andEmile Borel (1871-1956) from France, though their visit was not aimed at mathematics.Painlev´e had twice been the Prime Minister of France, in 1917 and in 1925. In 1920, hemade an official visit to China, leading a French delegation including Emile Borel. Atthat time, Borel was president of Ecole Normale Superieure.On July 1, 1920, Painlev´e was awarded an honorary doctorate by Peking University inBeijing. On that occasion, he gave a talk entitled
Mathematical Progress , which was the first mathematical talk given by a foreign speaker in China. Unfortunately, no math-ematical talk was given by E. Borel. In Shanghai, Painlev´e presented a talk
Scienceand Education in China at the Chinese Society of Sciences, in which he appealed Chi-nese scholars to organize societies in their own specialized fields. His appeal stimulatedChinese mathematicians to establish the Chinese Mathematical Society in 1935 (see Li[4]).On 12 October 1920, Bertrand Russell (1872-1970) arrived in Shanghai with his girl-friend. During his first three weeks in China, Russell delivered several public lectures inShanghai, Hangzhou, Wuhan and Changsha on topics ranging from Einstein’s relativitytheory to education and social problems. His lectures had influence on many Chinesesocial activists at that time and stimulated debates at newspapers. Zedong Mao (1893-1976) attended his talk in Changsha. Early in November, Russell arrived at his ultimatedestination, Peking University in Beijing. According to the schedule, he should lectureon problems of philosophy for six months.At the beginning of March 1921, invited jointly by the Society for Mathematics andPhysics at Peking University and by the Society for Mathematics, Physics and Chem-istry at Beijing Normal University, Bertrand Russell agreed to give four lectures onmathematical logic. The first lecture was given on 8 March to an audience of about150 professors and college students. The second lecture was announced for 15 March.Unfortunately, the day before, Russell came down with pneumonia and almost died.For nearly six weeks he was confined to his bed. He eventually recovered, but was stillvery weak when he left Beijing on 10 July 1921. Because of his sudden illness, Russell’ssubsequent lectures on mathematical logic were all cancelled. Nevertheless, his visit andtalks stimulated several Chinese to pursue mathematical logic (see Xu [9]).
3. Blaschke and Sperner at Peking University
In April 1932, as a part of his round-the-world mathematical tour to India, China,Japan and the United States of America, the German mathematician Wilhelm Blaschke(1885-1962) visited Peking University for two weeks. His book
Reden und Reisen einesGeometers contains an account of the whole tour. During the visit, he gave a series oftalks on differential geometry and integral geometry.At that time, there were very few people in Peking (Beijing) area who could under-stand differential geometry. One of them was professor Dan Sun (Guang-Yuan Sun,1900-1979) from Tsinghua University, who obtained his Ph.D from Chicago in 1928 witha thesis in differential geometry under the supervision of E. P. Lane. Another two wereShiing-Shen Chern and Da-Ren Wu (1908-1997) who were graduate students of professorSun working on their Master degrees at Tsinghua.Blaschke’s visit was not as sensational as Russell’s. Nevertheless, it was a big eventfor the Chinese mathematical community. According to [1], within the two weeks hewas invited to more than a dozen of banquets, from which he gained much weight. A lotof people came from other cities to attend his talks, even though many of them couldnot understand a word. On this occasion Chern first met Blaschke. He attended all thelectures, took detailed notes, and made his decision to study in Hamburg.After his brief visit, Blaschke recommended E. Sperner as a visiting faculty memberat Peking University for two years. He taught geometric foundation and topology, ranadvanced seminars, and supervised graduate students. At that time, the mathematicaldepartment had about seventy undergraduates and four graduate students. During hisvisit, Dr. Sperner also gave several talks at Tsinghua University and Nankai University.
When Shiing-Shen Chern finished his Master degree, he succeeded in the selectionexamination to study in abroad financed by the Boxer Indemnity. Usually, the studentssupported by the Boxer Indemnity should pursue their study and research in the UnitedStates. However, attracted by Blaschke, Chern decided to make his Ph.D in Humburg.Surprisingly, his application was approved by the Boxer Indemnity authority. In 1934,Shiing-Shen Chern arrived in Hamburg and enrolled as a Ph.D student of Blaschke.From there, he gradually stepped up the world mathematical stage.In fact, Da-Ren Wu also went to Hamburg a couple of years later. It was him whofirst introduced integral geometry into China.
4. Birkhoff and Osgood at Peking University
Modern mathematics was introduced into the United States of America in 1870s. TheAmerican Mathematical Society was founded in 1888. Both George D. Birkhoff (1884-1944) and William F. Osgood (1864-1943) belonged to the first generation of the globallyknown American mathematicians.In 1919, Li-Fu Chiang obtained his Ph.D from Harvard under the supervision of J.L. Goolidge. He was the second Chinese who ever made a Ph.D in mathematics. WhenChiang studied at Harvard, he was once an assistant of professor William F. Osgood whowas chairman of the mathematics department at that time. In 1919, Dr. Chiang wasappointed professor and founding chairman of the mathematical department of NankaiUniversity.At Nankai University, Tsai-Han Kiang (1902-1994) was one of the earliest studentsmajoring in mathematics. Supported by a Boxer Indemnity fellowship, he went to USAand obtained his Ph.D from Harvard in 1930 under the supervision of M. Morse. In1931, Dr. Kiang was appointed a professor at Peking University. Three years later, hewas appointed head of the mathematics department.In April 1934, arranged by Tsai-Han Kiang, professor George D. Birkhoff from Harvardvisited Peking University. During his visit, he gave a series of talks on several solutionsin quantum mechanics, differential equations of dynamics, four-colour problem, andaesthetic measurement. His talks were so fashionable that they attracted great interestamong both professors and students alike. However, since they were too advanced,almost no audience could understand them.In 1933, William F. Osgood retired from Harvard University, after being a professorthere for thirty years. Recommended by Li-Fu Chiang and invited by Tsai-Han Kiang, hecame to China and taught as a visiting professor at Peking University from 1934 to 1936.During his visit, contrary to Birkhoff, professor Osgood taught various basic courses onmechanics, real functions and complex functions. As assistants of the professor, PaoLu Hs¨u and Shu-Ben Sun made careful notes of the lectures. Afterwards, his lecturenotes
Functions of Real Variables and
Functions of a Complex Variable were publishedby Peking University (see Ding, Yuan and Zhang [2]).The long term visits of Sperner, Birkhoff and Osgood, in particular their basic math-ematics courses, made great inspiration and encouragement to the Chinese colleaguesand students. Their lecture notes were rare and valuable text books for years.
5. Wiener at Tsinghua University
From 1924 to 1930, Yuk-Wing Lee studied electrical engineering at Massachusetts In-stitute of Technology. In 1930, he obtained his Ph.D there under the supervision of professor V. Bush. During his MIT time, with the recommendation of his supervisor,Lee became an assistant and close friend of Norbert Wiener (1894-1964). In 1932, Dr.Lee returned to China and was appointed professor at the electrical engineering depart-ment of Tsinghua University. At that time, professor King-Lai Hiong was the head ofthe mathematics department. In 1934, based on the recommendation of professor Leeand professor Hiong, the president of Tsinghua University invited Norbert Wiener for along term visit. At the age of only forty, professor Wiener already made a name as amathematician. He was elected to the National Academy of Sciences, USA, in 1933.The Wiener family arrived at Tsinghua on 15 August, 1935. With the help of Yuk-Wing Lee, his family set up in the campus of Tsinghua University. In the next twosemesters, professor Wiener taught several courses on Fourier series, Fourier integrals,and Lebesgue integrals. To prepare the courses, based on his suggestions, the universitybought the related reference books in advance. His classes were very successful andattracted many faculty members and students alike, not only from Tsinghua, but alsofrom other universities in Beijing area. In particular, his classes paid more attention toraising problems and inspiring ideas rather than simply deducing theorems.Loo-Keng Hua never had a university education. However, through self-study hebecame one of the most important modern mathematicians in China. When Wienervisited Tisinghua University, Hua was an assistant at the mathematical faculty. Ofcourse, he attended all the courses of Wiener, kept discussing mathematics with him,and became friends with him. Gradually, by reading his papers, Wiener was impressedby his mathematical talent and offered to recommend him to G. H. Hardy in Cambridge.In 1936, supported by a Boxer Indemnity fellowship, Loo-Keng Hua went to CambridgeUniversity for two years, which became a turning point for his mathematical career.Besides his lectures in mathematics department, professor Wiener continued to workwith Dr. Lee on problems of electric-circuit design. They tried follow in the footstepsof Bush in making an analogy-computing machine, but to gear it to the high speed ofelectrical circuits instead of to the much lower one of mechanical shafts and integrators.In fact, when Wiener accepted the invitation, the chairman of the electrical engineeringdepartment asked him for help to buy an analogy-computing machine in USA for Ts-inghua University. Unfortunately, it was too expensive and Tsinghua could not afford it.Anyway, Wiener spoke highly of his visit to China. He wrote in his book [8] “If I wereto take any specific boundary point in my career as a journeyman in science and as insome degree an independent master of the craft, I should pick out 1935, the year of myChina trip, as that point.” In the book, he also wrote in detail about his impression ofthe Chinese people, their culture, beliefs and daily life.The Wiener family left China on 19 May, 1936, for the International Congress ofMathematicians in Oslo. He maintained lasting friendships with his Tsinghua colleagues,in particular with Loo-Keng Hua and Yuk-Wing Lee, and provided his support wheneverit was needed. Based on his recommendation, John von Neumann was much interestedto visit China. Unfortunately, the Japanese invasion in 1937 made it no longer possible.
6. Hadamard at Tsinghua University
On 22 March, 1936, Jacques Hadamard (1865-1963) and his wife arrived in Shanghai bypassenger ship the
Queen of Asia . When the ship stopped at the wharf, representativesof the Chinese Mathematical Society, the Chinese Physical Society and the Sino-FrenchFriendship Association got on board to greet them. In the evening, president Yuan-PeiCai of Academia Sinica gave a banquet to welcome them. Many famous scientists andscholars in Shanghai attended the welcome banquet. In the following days, professor
Hadamard gave a couple of public lectures at Chiao Tung University and Sino-FrenchFriendship Association, respectively.At that time, both Hadamard and his wife were about seventy. Therefore, beforetheir departure, they were a little worried about their health and the security in Beijing.To make sure the security situation, he wrote to Norbert Wiener who had been therealready for one semester. Of course, he obtained a warm confirmation.On 7 April, 1936, they arrived in Beijing by train. The Hadamards were greeted by thepresident of Tsinghua University, the dean of science and the chairman of mathematicsdepartment at the railway station. At that time, professor King-Lai Hiong was thechairman who motivated the invitation and made the arrangement.According to the plane, professor Hadamard would give twenty lectures on definiteproblems of partial differential equations. It was the first time that partial differentialequations was systematically taught in China. Of course, he also gave public mathe-matical talks on different occasions. For example, on the 25th anniversary of TsinghuaUniversity, he lectured on some reflections on the role of mathematics.
His talks weregreat inspiration to the audience, in particular to the young faculty members and stu-dents.Everybody knows that the prime number theorem was first proved by Jacques Hadamardand Charles-Jean de la Vall´ee Poussin respectively in 1896. Although his mathematicalinterest already shifted to partial differential equations and other subjects, Hadamardhimself was a great master in number theory. When he was at Tsinghua, he quickly gotto know Loo-Keng Hua and impressed by his mathematical talent and his persistencyin the subject. While discussing the Waring problem with Hua, Hadamard introducedVinogradov’s work to him. Afterward, Hua wrote to Vinogradov and made a life longfriendship with him. Along with Norbert Wiener, professor Hadamard also persuadedchairman Hiong to support Loo-Keng Hua go abroad to improve his mathematics.Besides Loo-Keng Hua, professor Hadamard also helped several other young Chinese.With his recommendations, both Xin-Mou Wu and Chi-Tai Chuang went to Paris sup-ported by the Boxer Indemnity. Wu studied partial differential equations with professorsH. Villat and Hadamard. He returned to China in 1951 and became one of the PDEpioneers in China. Chuang obtained his Ph.D in 1938 under the supervision of professorG. Valiron from University of Paris. He returned to China in 1939 and became a leadingexpert in complex functions in China.When Hadamards arrived at Tsinghua, the Wiener family was still there. The twogreat men had a lot of mathematical discussions and the two families had many happytimes together. Both Hadamard’s biography [6] and Wiener’s autobiography [8] gaveaccounts on their experiences in Beijing. Wiener wrote “We used to go to town tovisit the Hadamards and sometimes Margaret and I, or Lee and the two of us, used togo down into the tangled, squalid streets of the socalled Chinese city (as opposed tothe rectangular Tatar city) to rummage in the antique shops. There we would oftencome across ancestor portraits which show dignified Chinese gentlemen or ladies, in stiffposes, with hands on the knees, dressed in marvelous silken gowns, which for the menwere robes of office, civil or military. For all their pomp and stiffness, it was commonfor the faces in these pictures to be of a remarkable fineness, humor, and sensitivity. wefound one such ancestor portrait which was so like Professor Hadamard himself, with hissomewhat sparse, stringy beard, his hooked nose, and his fine, sensitive features, thatit would have been completely adequate to identify him and to pick him out of a largeassembly of people. There was, it is true, a very slight slant to the eyes, and a very slightsallowness of complexion, but not enough to confuse the identification. We bought this picture and gave it to its likeness. He appreciated it very much, but I don’t think thatMme. Hadamard cared for it.”When the Chinese Mathematical Society was founded in 1935, it decided to launchtwo journals
Acta Mathematica Sinica and
Journal of Mathematics , the first for originalworks and the second for introductional reports. To support the Chinese mathematicalcommunity, both professor Wiener and professor Hadamard published papers at theearly issues of the Acta.On 25 June, 1936, professor Hadamard finished his Chinese visit and left Beijing forParis with his wife by the Trans-Siberian Railway. His visit had lasting impact on themathematical development in China.
Acknowledgements.
This work is supported by the National Natural Science Foun-dation of China (NSFC11921001) and the National Key Research and DevelopmentProgram of China (2018YFA0704701).
References
1. W. Blaschke,
Reden und Reisen eines Geometers . VEB Deutscher Verlag Der Wissenschaften, Berlin,1961.2. S. S. Ding, X. D. Yuan and Z. G. Zhang, Eighty years of Mathematics Department of PekingUniversity (in Chinese),
China Historial Materials of Science and Technology , (1993), No.1, 74-85.3. B. Koopman, William Fogg Osgood - In Memoriam. Bull. Amer. Math. Soc. (1944), 139-142.4. W. Li, Jacques Hadamard in China. ICCM Not. (2014), No. 2, 69-74.5. Q. Liu, Exchange of mathematical thoughts between China and foreign countries in the 20th century (in Chinese), Science Press, Beijing, 2010.6. V. Maz’ya and T. Shaposhnikova,
Jacques Hadamard, A Universal Mathematician . American Math-ematical Society, Providence, RI, 1998.7. J.-C. Martzloff,
A History of Chinese Mathematics , Springer-Verlag, Berlin Heidelberg, 1997.8. N. Wiener,
I am a mathematician . Doubleday and Co., New York, 1956.9. Y. Xu, Bertrand Russell and the introduction of mathematical logic in China,
History and Philosophyof Logic , (2003), 181-196.10. D. Zhang, The Development of Modern Mathematics in China (in Chinese), Hebei Science andTechnology Publishing House, Shijiazhuang, 1999.11. Y. Zhang,
China Mathematical History Research in 20th Century (in Chinese), Harbin Institute ofTechnology Press, Harbin, 2016.12. C. Zong,
Modern Mathematics in China , in preparation., in preparation.