H. W. Gould

The passing of Kai Lai Chung(鍾開來/钟开莱) on 1 June 2009 at the venerable age of 91 reminds me forcibly of the importance of Chung's work in my own life.

Chung posed a combinatorial identity as Problem 4211 in the American Mathematical Monthly, Vol. 53(1946), Aug.-Sept. issue, p. 397, which remained without a published solution until I published a solution ten years later. See Amer. Math. Monthly. Vol. 63(1956), Feb. issue, pp. 126-127, where the reference is to my paper "Some generalizations of Vandermonde's convolution" in same issue of the Monthly, pp. 84-91. This was the second paper I published and the first one where I summarized some generalizations that were not well known in the mathematics literature, and which I traced back to the work of Heinrich August Rothe in 1793. Not many people knew much about combinatorial identities in the 1940-50 times. I sent my solution of Problem 4211 to Chung and he suggested that I should publish it. He also sent me a more general research question that has had an impact on my own research work. This problem is related to questions raised by eminent (late) Chinese mathematician Pao Lu Hsu (or Xu Bao-Lu/许宝騄) (1909-1970), whose work I admired also. Pao Lu was in Beijing and before L. C. Hsu wrote to me in 1965, I was not able to communicate with him. The problem offers still more avenues for further research even today. From time to time I would correspond with Kai Lai and admired his work. Just in recent years he asked me for a proof of an identity.

In 1965, seven years before U. S. President Nixon visited China to meet Chairman Mao, I began a collaboration with distinguished Chinese mathematician L. C. Hsu (Xu Li-Zhi/徐利治), then at Jilin University, Changchung, Peoples' Republic of China, who had written to me. We then published a joint paper in 1973 in the Duke Mathematical Journal that generalized many special combinatorial inversion theorems and that has sparked much further research. This was certainly one of the very first (if not the first) joint modern publications between USA and PRC mathematicians. Hsu is somewhat younger than Chung. However Hsu told me he had been a student of Chung many years before in China. Hsu visited me, staying at my home, and sent his daughter to study here, and invited me to be an associate editor of a journal he established at Dalian (Journal of Mathematical Research and Exposition/ Shu Xue Yan Jiu Yu Ping Lun / 数学研究与评论).

In the same way that I had not thought of publishing my very first paper in 1954, until Emil Grosswald and Leonard Carlitz urged me to do so, I am indebted to Kai Lai Chung for encouragement.

I studied Chinese writing as a youngster, memorizing several thousand characters, and then took regular classes in written and spoken Chinese circa 1988.

I have always felt it a great honor to work with Chinese mathematicians and assist with their work.

Kai Lai Chung influenced my work and I feel the world of mathematics has suffered a great loss with his passing but we have been enriched so much because he lived and did mathematics and helped people.

13 August 2009

Note: This memorial item has also been published in the Journal of Mathematical Research and Exposition,

Dalian, PRC, Vol. 29(2009), No. 6, pp. 952-953.

19 Nov. 2009