ISSN 1923-8444 [Print] Studies in Mathematical Sciences ISSN 1923-8452 [Online] Vol. 6, No. 2, 2013, pp. [71{82] www.cscanada.net DOI: 10.3968/j.sms.1923845220130602.907 www.cscanada.org The Intellectual Journey of Hua Loo-keng from China to the Institute for Advanced Study: His Correspondence with Hermann Weyl Jean W. Richard[a],* and Abdramane Serme[a] [a] Department of Mathematics, The City University of New York (CUNY/BMCC), USA. * Corresponding author. Address: Department of Mathematics, The City University of New York (CUN- Y/BMCC), 199 Chambers Street, N-599, New York, NY 10007-1097, USA; E- Mail: [email protected] Received: February 4, 2013/ Accepted: April 9, 2013/ Published: May 31, 2013 \The scientific knowledge grows by the thinking of the individual solitary scientist and the communication of ideas from man to man Hua has been of great value in this respect to our whole group, especially to the younger members, by the stimulus which he has provided." (Hermann Weyl in a letter about Hua Loo-keng, 1948).y Abstract: This paper explores the intellectual journey of the self-taught Chinese mathematician Hua Loo-keng (1910{1985) from Southwest Associ- ated University (Kunming, Yunnan, China)z to the Institute for Advanced Study at Princeton. The paper seeks to show how during the Sino C Japanese war, a genuine cross-continental mentorship grew between the prolific Ger- man mathematician Hermann Weyl (1885{1955) and the gifted mathemati- cian Hua Loo-keng. Their correspondence offers a profound understanding of a solidarity-building effort that can exist in the scientific community. Her- mann Weyl had a profound influence on Hua Loo-keng and facilitated his coming to the Institute for Advanced Study at Princeton. Hua Loo-keng who left school at the age of fifteen was able to produce considerable work in number theory, algebra, geometry, and complex analysis. Hermann Weyl had interests that covered wide subfields of mathematics and was also involved in the development of general theory of relativity alongside Albert Einstein. yHistorical Studies-Social Science Library of the Institute for Advanced Study at Princeton, School of Mathematics|Member Series, 1978{1983, Box: Harris{Kurihara. zSouthwest Associated University was a merger of three universities during the Sino-Japanese war. 71 The Intellectual Journey of Hua Loo-keng from China to the Institute for Advanced Study: His Correspondence with Hermann Weyl Key words: Hua Loo-keng; Hermann Weyl; Scientific exchange between China and the United States of America; The Institute for Advanced Study at Princeton; Southwest Associated University Richard, J. W., & Serme, A. (2013). The Intellectual Journey of Hua Loo-keng from China to the Institute for Advanced Study: His Correspondence with Hermann Weyl. Studies in Mathematical Sciences, 6 (2), 71{82. Available from http://www.cscanada.net/index.php/ sms/article/view/j.sms.1923845220130602.907 DOI: 10.3968/j.sms.1923845220130602.907 1. INTRODUCTION This paper aims to show an unlikely friendship that had developed between Her- mann Weyl (1885{1955), one of the most prolific mathematicians of the twentieth century, and the self-taught Chinese mathematician Hua Loo-keng (1910{1985). Hermann Weyl was not only responsible for helping to bring Hua Loo-keng to the Institute for Advanced Study, but was instrumental in helping him publish several papers in leading international mathematics journals. Their correspondence1 and work together in the nineteen-forties, a time of war for both America and China, tell a valuable story of scientific courage and solidarity, and shows that culture, nation, and identity are no obstacle to the furthering of intellectual knowledge. Hua Loo-keng, born in Jintan in the Jiangsu province of China, left school due to his parents' financial difficulties and did not complete high school. While helping his parents managing a small grocery store, Hua Loo-keng taught himself mathematics and published two papers in a Shanghai science periodical. One of the papers was a critique (On the incorrectness of Su Jia Ju's paper) of an article published by a Chinese mathematician who claimed to have a solution for the quintic equation. Those papers brought Hua Loo-keng to the attention of Xiong Qinglai2, the chairman of the mathematics department at Tsing Hua University in Beijing. In 1931 Xiong Qinglai invited Hua Loo-keng to work as \a special Assistant" [1] in the mathematics department. Hermann Weyl as a mathematician had interests that covered wide subfields of mathematics and was also involved in the development of general theory of rela- tivity alongside Albert Einstein. He was the first mathematician to formulate the concept of \gauge invariance" [2] which would revolutionize physics during the sec- ond part of the twentieth century and was a major contributor in the field of Lie Algebra. Accordingly \gauge invariance" means that only invariant relations under transformations are geometrically significant. A concise history of the development of mathematics in China offers a key to appreciating the genuine solidarity and support that Hermann Weyl manifested 1 Around the mid-1940's, Hua Loo-keng, while teaching at the Southwest Associated University began a correspondence with Hermann Weyl. Their correspondence ranged from Weyl helping Hua Loo-keng publishing several articles in international mathematical journals to Weyl seeking to bring Hua as a researcher to the Institute for Advanced Study at Princeton. While Hua Loo- keng was at the Institute, Weyl sent an open letter to different universities to secure him a teaching position. 2 Xiong Qinglai who visited France in 1931 followed Jacques Hadamard's lectures at that time [9]. Jacques Hadamard (1865{1963) was a French mathematician who did considerable works in \func- tion theory, calculus of variations, number theory, analytical mechanics, algebra, geometry, prob- ability theory, elasticity, hydrodynamics, partial differential equations, topology, logic, education, psychology, and the history of mathematics" [6]. 72 Richard, J. W., & Serme, A./Studies in Mathematical Sciences, 6 (2), 2013 towards Hua Loo-keng. The development of mathematics in China and its partic- ipation among the international mathematics community followed different paths based on three historical periods: (a) The period of foreign missionaries, when cer- tain mathematical texts were translated into Chinese, (b) The period when Chinese students who expressed interest to study went abroad to Japan, (c) The period where using the funds of the China Foundation for the Promotion of Education and Culture, Chinese students started to travel to Europe and the United States of America [3]. It was also during this period that European and American professors were invited to lecture at Chinese Universities. Among the professors who visit- ed China to lecture, where notable mathematicians such as George Birkhoff, Paul Painleve, Jacques Hadamard, Emmanuel Sperner, Norbert Wiener, Emile Borel. During this period, there was a prevalence of Chinese students or mathemati- cians who went abroad to further pursue their mathematical interests. One of the mathematicians who had the most impact on the field of mathematics in China as well as its overall scientific development is Hua Loo-keng. The correspondence between Hua Loo-keng and Hermann Weyl demonstrates the collaboration, support and genuine solidarity that can exist between mathematicians or scientists. This correspondence is also a proof of the mathematical exchanges that took place be- tween the United States of America and China. In the history of mathematics, Hermann Weyl was special. He was not only a great mathematician but according to Michael Atiyah: \Weyl was always keen to identify talent and provide encour- agement for the younger generation" [4]. Weyl spent many years trying to bring Hua Loo-keng as a Fellow at the Institute for Advanced Study at Princeton, the environment in which he found himself amidst scientists like Robert Oppenheimer a physicist considered by many to be the father of the atomic program in the United States of America, Albert Einstein, James Waddell Alexander, Marston Morse who created Morse theory, Atle Selberg, Carl Ludwig Siegel, Solomon Lefschetz. 2. HUA LOO-KENG: JOURNEY FROM SOUTHWEST AS- SOCIATED UNIVERSITY (KUNMING, YUNNAN, CHI- NA) TO THE INSTITUTE FOR ADVANCED STUDY AT PRINCETON Hua Loo-keng a renowned self-taught mathematician left school at the age of fifteen, so he could help his father manage the family grocery store. Early in his career he was invited to Tsing Hua University to work as a clerk in the mathematics depart- ment and in the library. Hua Loo-keng produced mathematical papers that brought him to the attention of Norbert Wiener [5], the American mathematician, who had accepted an invitation to lecture at Tsing Hua University. With Wiener's help, Hua Loo-keng spent one year at Cambridge University under the guidance of the famous mathematician Godfrey Harold Hardy. Later, Hua Loo-keng returned as a full professor at Southwest Associated University. While at Kunming, Hua Loo- keng initiated research on what he called the \geometry of matrices" and established correspondence with the mathematician Hermann Weyl, who at the time was at the Institute for Advanced Study at Princeton. What transpired through this corre- spondence is a relationship of mentor, support and guidance from the renowned and established mathematician Hermann Weyl, to the gifted Hua loo-keng. This corre- 73 The Intellectual Journey of Hua Loo-keng from China to the Institute for Advanced Study: His Correspondence with Hermann Weyl spondence also offers a deeper understanding of a solidarity-building effort among the scientific community. A student of David Hilbert, the founder of the G¨ottingenschool of mathematics, Hermann Weyl (1885{1955), had developed interests in various areas of mathematics as well as the theory of relativity [6]. Weyl's interests in mathematics range from the foundations of mathematics to geometry, analysis, Riemann surfaces, and topology.