In 2017, the project entitled “Geometry, analysis and computation on manifolds” was funded by the National Natural Science Foundation of China (NSFC) as one of first three “Basic science research center projects”. In order to support this project, the Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences set up the Hua Loo-Keng Center for Mathematical Sciences (HCMS) on the 20^th, March, 2017. HCMS established a research team including Zhou Xiangyu, Xi Nanhua, Guo Lei, Yuan Yaxiang, Sun Binyong, Chen Zhiming, Zhang Ping, Gao Xiao-Shan, Gong Fuzhou, Huang Feimin, Wang Yuefei as well as about 50 young members.

In the past five years, the research team made important breakthroughs and progresses on the BSD conjecture, the Navier-Stokes equation, and the Langlands Program; solved some important mathematical problems such as the Kazhdan-Mazur's nonvanishing hypothesis and the conjecture of Heinloth–Ngô–Yun on the functoriality between different Kloosterman Gˇ-local systems; established the study on the transcendental method of complex analysis, the method of parallel manifold optimization, and the theoretical foundation of PID control and made important applications in the design of aerospace controllers.

HCMS has stably supported and cultivated a young and energetic research team in the fields of geometry, analysis and computation on manifold, especially the group of outstanding young talents under the age of 40. During the project, Chen Zhiming, Sun Binyong, and Zhang Ping were elected academicians of the Chinese Academy of Sciences, 9 members were supported by the NSFC for Distinguished Young Scholars, 8 members were supported by the NSFC for Excellent Young Scholars, and 10 members were supported by the Research Fund of International Young Scientists, etc. The members of the HCMS have won more than 50 honors and awards, including 2 Second Prizes of National Natural Science Awards, the Hendrik W. Bode Lecture Prize by the IEEE Control Systems Society, 2 National Innovation Awards, SIAM Prize for Distinguished Service to the Profession, CSIAM Su Buchin Prize, CSIAM Wu Wentsun Prize, CMS Shiing Shen Chern Mathematics Award, Wu Wenjun Artificial Intelligence Science and Technology Award, etc.

Besides, HCMS allocated special funds every year to carry out high-level international cooperation. By inviting the outstanding experts in related fields at home and abroad, especially those outstanding young researchers, new ideas were generated to promote the solution of major problems. These open activities played a radiating role during the implementation of this project. In the past five years, HCMS has hosted 3 academic years, 14 special seminars and more than 50 frontier seminars.

In 2022, the project of “Geometry, analysis and computation on manifolds” was renewed by the NSFC for another five years.