AWARDEE OF MATHEMATICS AND MECHANICS PRIZE

KE ZHAO

Abstract

Ke Zhao ( C. Ko), mathematician, born on April 12, 1910 in Wenling, Zhejiang Province.  He graduated from the Department of Mathematics in Tsinghua University in 1933.  He continued his study of mathematics under the supervision of Prof. Mordell (FRS) and received his Ph. D. Degree from The University of Manchester, England, in 1937.  The next year, he came back to China.  He successively served as professor in Chongqing University as well as professor and president of Sichuan University.  He was elected as a member of Chinese Academy of Sciences in 1955. Now, he is the honored President of Chinese Society of Mathematics.
Prof. Ke has made important contributions to number theory, algebra as well as combitorial theory.
1. A thorough study of positive definite quadratic forms
Ke published a series of papers on the subject. He successively clarified the representation of a quadratic form as sum of squares of linear forms; determined the class number of positive quadratic forms of determinant 1 and obtained decomposition of quadratic forms in various variables.
2. “Ko theorem " in Diophantine equation
In 1842 Catalan proposed a conjecture: 8 and 9 are the only two successive integers,  which are all powers of positive integers.  Ke proved that there are no positive integral solutions for the equation x2-1 =yn if xy≠0, when n>3. This is a breakthrough in the field.  So, Mordell cited the result as “Ko theorem" in his monograph “The Diophantine Equations". The method introduced by Ke in his proof has been adopted by other scholars in various branches in number theory.
3. “Erdos-Ko-Rado theorem" in combitorial theory
The paper “Intersection theorem for systems of finite sets" co-authored by Erdos, Ke and Rado in 1961 is of fundamental importance in extremal combinatorics and was the starting point of researches in the field, as cited by Frankl and Graham. Now it is well known as “Erdos-Ko-Rado theorem".
Prof. Ke's various significant results, like the “Erdos-Ko-Rado theorem”, have been highly regarded and widely cited in mathematics community.  He has devoted himself to the mathematics education in China for over 60 years and fostered a number of mathematicians.