(1) Founding In June 1950, the Institute of Mathematics was under preparation soon after the Chinese Academy of Sciences (CAS) was founded, and many things were waiting to be done. The preparation office was located at No.3 Wenjin Street in Beijing. The wellknown mathematician Su Buqing was the director, Zhou Peiyuan, Jiang Zehan, Hua Luogeng and Xu Baolu were the deputy directors of the office, and Tian Fangzeng was the secretary. The central government of the country attached great importance to the founding of the institute. In January 1951, the State Council approved the appointment of Hua Luogeng as the director of the Institute of Mathematics to be founded. In July 1, 1952, the institute was established and located on the campus of Tsinghua University. The institute decided to focus its research on coordinated development of pure mathematics and applied mathematics. The first research groups were set up to study number theory, differential equations, mechanics, computer development, probability and statistics, algebra, and topology. In the first half of 1953, there were 32 researchers in the institute, including 5 research professors (Hua Luogeng, Min Naida, Wu Xinmou, Zhang Sucheng, Wu Wenjun), 5 associate research professors (Guan Zhaozhi, Tian Fangzeng, Wang Shouren, Zhuang Fenggan, Xia Peisu), 6 assistant research professors (Lin Hongsun, Sun Yifeng, Yue Minyi, Feng Kang, Wan Zhexian, Hu Haichang), 11 research trainees (Lu Qikeng, Gong Sheng, Hu Hesheng, Zhang Liqian, Wang Guangyin, Qiu Peizhang, Ding Xiaqi, Xu Kongshi, He Shanyu, Sun Hesheng, Wang Yuan), and 5 joint research professors (Su Buqing, Chen Jiangong, Duan Xuefu, Hu Shihua, Zhang Zongsui). The directions they started laid foundations for the development of the institute. Only among those 32 people, 17 were elected academicians (Members) of the CAS.  
(2) Marching Towards Science In 1956, the state formulated the 12Year Program for the Development of Science and Technology. While ensuring a coordinated development of major aspects of mathematical research, the Institute of Mathematics prioritized the development of differential equations, probability and statistics, which were closely related to the national economy and national defence. It also set up the research groups on functional analysis and mathematical logic to intensify the theoretical study of relevant subjects. In 1957, Professor Xiong Qinglai, who returned from France, founded the research group of the theory of functions. In this period, the research work related to mechanics and computer development managed affairs on their own to build the Institute of Mechanics and the Institute of Computing Technology of the CAS. Encouraged by the 12Year Program for the Development of Science and Technology, the institute started its march towards science. In 1956, China granted the first National Natural Science Award. Of the three top prizes, the Institute of Mathematics won two. The institute was temporarily moved to Xiyuan Hotel in 1957. In the next year, it was moved to Zhongguancun (the northern building of the Institute of Computing Technology). In 1961, research divisions were set up according to subjects, including "four branches" (number theory, algebra, geometry, topology), function theory, differential equations, functional analysis, mathematical logic, theoretical physics, probability and statistics. The Division of Operations was formed with related groups in the Institute of Mechanics and the Institute of Mathematics proposed by Qian Xuesen, Hua Luogeng and Xu Guozhi. In 1962, responding to the needs of our country, the Division of Control Theory was established under the leadership of Guan Zhaozhi and Song Jian. Later, the Division of Mechanics was reestablished. The research work in various directions carried forward rapidly. From 1961 to 1965, following the policy of gaining both achievements and talents, the institute had a relatively stable developing period preparing for the future. After the "cultural revolution" started in 1966, all research stopped. In 1972, Premier Zhou Enlai gave instruction on intensifying basic research, so mathematical research started again. In 1973, Chen Jingrun made public his result on the Goldbach conjecture. In 1975, Yang Le and Zhang Guanghou published their result on the value distribution theory. The finite element algorithm, founded by Feng Kang et al. in the early 1960s independently of the West, was applied widely in many branches of the national economy and national defence. These were the symbolic achievements of mathematical research of our institute's scientists who had been working at an extremely difficult time.
(3) Springtime of Science After the "gang of four" was smashed in 1976, especially after the National Science Congress was held in 1978, China greeted a springtime of science. At such a time when knowledge is respected and talents are honored, the researchers of the institute spared no efforts to keep up with the latest development of mathematical study, making rapid headway in pure and applied mathematics and pushing China's mathematical study onto a track of healthy development. In 1977, the Computing Center of the CAS, mainly engaged in the research of computational mathematics, was established and located at No.4 South 4th Street, Zhongguancun. From this the Institute of Computational Mathematics and Scientific/Engineering Computing was formed in 1995. The successive directors of the institute were Feng Kang, Shi Zhongci, Cui Junzhi, and presently Yuan Yaxiang. At the end of 1979, the CAS decided to separate part of the personnel from the Institute of Mathematics to set up the Institute of Systems Science, whose task is to study control theory, operations and management, statistics, systems engineering, and related boundary sciences of mathematics. The successive directors of the institute were Guan Zhaozhi, Cheng Ping, Chen Hanfu, and presently Guo Lei. Part of the personnel of the Institute of Mathematics was merged with the former Promotion Office of Applied Mathematics of the CAS to form the Institute of Applied Mathematics. The successive directors of the institute were Hua Luogeng, Wu Fang, Zhang Xiangsun, and presently Ma Zhiming. The Institute of Mathematics mainly focuses on basic theoretical research as well as applied mathematics and computer science. Its successive directors were Hua Luogeng, Lu Qikeng (executive vicedirector), Wang Yuan, Yang Le, Long Ruilin, Li Bingren (acting director), and presently Wang Yuefei. The researchers in the four institutes have been working on different subjects while maintaining good cooperation, resulting in a large number of achievements and talents. In 1982, when the state resumed the granting of the National Natural Science Award, the four institutes were again in the spotlight with their highlevel scientific results. In 1991, the later three institutes were moved to No.A1, South 4th Street, Zhongguancun.
Picture 6 S.S.Chern visited the institute and made a speech. (4 ) Historical Opportunities In December 1998, as part of the National Knowledge Innovation Program of the CAS, the Institute of Mathematics, Institute of Applied Mathematics, Institute of Systems Science and Institute of Computational Mathematics and Scientific/Engineering Computing were merged into the Academy of Mathematics and System Sciences (AMSS). Yang Le is the president and Zhang Xiangsun is the executive vicepresident of the AMSS. Since its founding, the AMSS has launched a series of major reforms, especially in adjusting structure and transforming the management mechanism; condensing research subjects and clarifying the main targets; improving the environment of the compound and building innovation culture. The work has been proceeding rapidly, and achieving obvious results. The knowledge innovation program has brought about new opportunities to the development of mathematics and system sciences. The Institute of Mathematics set up the Division of Basic Mathematics, the Division of Nonlinear Analysis, the Young Research Center of Geometric Analysis, the Division of Computer Science, and the Morningside Center of Mathematics. The Institute of Applied Mathematics set up the Division of Operations, the Division of Probability and Statistics, the Division of Differential Equations and Computing, and the Division of Decision and Information Science. The Institute of Systems Science set up the Key Laboratory of Systems and Control, the Key Laboratory of Management, Decision and Information Systems, the Division of Statistical Science, the Division of Pure and Applied Mathematics, and the Mathematics Mechanization Research Center. The Institute of Computational Mathematics and Scientific/Engineering Computing set up the State Key Laboratory of Scientific and Engineering Computing. The AMSS has built the Laboratory of Graph Theory and Combinatorics, the Research Center of Decision Making under Uncertainty, and the Information Security Center. The AMSS is also preparing to build the Research Center of Dynamic Systems, the Research Center of Financial Mathematics, the Research Center of Biological Information, etc. These research centers go beyond a single branch and reflect new increasing interests. They are in keeping with the strategic requirements of our country, and will help to promote interdisciplinary sciences. The Chinese Mathematical Society, the Operations Research Society of China, the Systems Engineering Society of China et al. set up their offices in the AMSS. The AMSS sponsor 14 academic journals.
Picture 1 The inaugural meeting of AMSS 
In the past 50 years, the scientific personnel of the four institutes has made important contributions to the country's development of mathematics and system sciences as well as the construction in national economy and national defence. They have won more than 400 scientific awards, including one National Top Science and Technology Award, four firstclass prizes of the National Natural Science Award, and some important international awards. Some important research achievements in applied sciences have been acknowledged by the central government leaders and relevant divisions of application. This has proved the important role of mathematical theory in the main fronts of the national economy.
Chairman Jiang Zemin vested Wu Wentsun the first
National Top Science and Technology Award.
National Science & Technology Progress Award (second class)
CAS Science & Technology Achievement Award (first class)
CAS Science & Technology Progress Award (first class)
The AMSS now has 15 CAS academicians and two CAE (Chinese Academy of Engineering) academicians. Photos 85101 show CAS academicians Wu Wenjun, Wang Yuan, Yang Le, Lu Qikeng, Ding Xiaqi, Wan Zhexian, Shi Zhongci, Lin Qun, Chen Hanfu, Ma Zhiming, Ding Weiyue, Yan Jiaan, Lu Ruqian, Li Banghe, Guo Lei, and CAE academicians Cui Junzhi, Liu Yuanzhang.
Academicians who have passed away are Hua LooKeng, Zhang Zongsui, Feng Kang, Guan Zhaozhi, Chen Jingrun and Xu Guozhi.
Researchers who worked at the Institute of Mathematics and were later elected academicians are Su Buqing, Chen Jiangong, Duan Xuefu, Zhuang Fenggan, Hu Shihua, Dai Yuanben, Hu Haichang, Hu Hesheng, Song Jian, Xia Peisu and Tang Zhisong.
Since 1956, the Institute of Mathematics has increased the exchanges with domestic institutions of higher learning through holding training sessions and receiving teachers for training. Many mathematicians from universities benefited from the training and later became mainstays of various fields. The international cooperation and exchanges in the 1950s were mainly conducted with the socialist countries. After the reform and openingup policy began in 1978, a large number of researchers went abroad and engaged in cooperative research and extensive exchanges with foreign counterparts. In 1985, advocated by Director Wang Yuan, the Institute of Mathematics became one of the first institutes of the CAS that were opened to foreign scientists. Soon, the other three institutes also set up open laboratories, which received visiting scholars from both home and abroad in light of the principle of "opening, flowing, integrating, and gearing the research to the country and the world". In recent three years, 719 person/times of visits abroad were made by researchers of the AMSS, who also received 1,055 visitors (including 604 overseas scholars and 451 domestic visitors). From 1999 to 2001, the AMSS also sponsored or cosponsored 25 major international conferences or seminars. More than 70 academic workshops are being held regularly every year.  
 
 
Picture 10 The Institue of Mathematics engaged S.S.Chern as an honorary professor. 
The Institute of Mathematics has a fine tradition of respecting teachers, of valuing education, and of attaching great importance to personnel training. The institute once set up a "boxing practicing field" for young scholars to exchange views. In 1956, the institute enrolled the first batch of graduate students. But before the "cultural revolution," less than 20 people were enrolled for the graduate study. In 1978, the graduate study system was resumed, and the institute enrolled 24 graduate students selected from more than 1,500 people. Since then, personnel training had been systemized, and the institute became a key base of the CAS to train students toward doctor's degree. Since 1978, nearly 1,000 students got the master's degree, more than 500 students got the doctor's degree, and more than 100 scholars conducted postdoctoral study in the four institutes. A number of outstanding young mathematicians have emerged. Three of them were elected academicians of the CAS; two were honored as "Top Ten Outstanding Youth"; two won the Young Scientist Award of China; one won the National May 4th Medal; three became chief scientists of "973" projects; 20 obtained the financial support from the State Outstanding Youth Fund; 8 won Hong Kong's "Qiushi" Award for Outstanding Young Scholars; 10 won the firstclass prize of the CAS Young Scientists; and 17 were supported by the "Hundred Talents Program".  
Picture 1 Professor Xu Guozhi and his students.  

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