The Key Laboratory of Mathematics and Its Applications of Peking University was established in 1989. In 1994, the laboratory was approved as the key laboratory of the State Education Commission (now the Ministry of Education). In the assessment of key laboratories of the Ministry of Education in 2015, the Key Laboratory of Mathematics and Its Applications of Peking University received a rating of "excellent"  and was rated number one in the section of mathematics and mechnics.

The primary focus of the Key Laboratory of Mathematics and Its Applications is to make outstanding contributions to the development of national mathematics with excellent investigators, the original innovations, theoretical research and applied research simultaneously. The objective of the lab is to accommodate geniuses from all over the world, provide indispensable training and ultimately to send talents to universities and research. Concentrating on attracting and developing young scientists at an international level of comprehensive competency, to promote the excellence in the overall level of scientific research, to strengthen communication and cooperation with various scientific research groups around the world.

The laboratory has an excellent academic atmosphere and tradition for fostering young talents. Through the combination of seminars and workshop, academic leaders in the Key Laboratory has produced the excellent condition that enables the young researcher to grow as quickly as possible. Such leaders include Academician of the Chinese Academy of Sciences, senior Yangtze River Scholars and the Distinguished Young Scholars of NSFC. Lab member Prof. Huijun Fan and Prof. Xiaobo Liu jointly organised the symplectic geometry and mathematical physics seminar, promoted the development of this emerging field, formed a strong new research direction, trained new talents for Peking University and even influenced on domestic mathematics society. In addition to young talents project, post-doctoral training program also is paid great attention. In last five years, more than 40 post-doctoral researchers were funded and most have joined universities, research institutes around the world.

Facilitating these achievements are compulsory courses and special courses for undergraduate and postgraduate students from the School of Mathematical Science which are implemented by lab professionals. The combination of a great academic environment coupled with these courses allows for the forging of future academic leaders. Evidenced by the many undergraduates which participate in undergraduate research projects each year and furthered by the many excellent students who win gold medals in the International Mathematical Contest in Modelling and the Interdisciplinary Contest in Modelling.

To promote high level and substantive academic exchange and cooperation, the laboratory frequently organises large academic seminars where outstanding mathematicians from home and abroad are invited to present their most recent achievements in various fields. Between 2012 and 2017, several world-famous mathematicians were invited to visit the laboratory and carried out intensive collaborations. Such collaborators include: Fields Medal winners Bao Chau Ngo, A. Okounkov, S. Smale, E. Zelmanov; Wolf Prize winner Phillip A. Griffiths; Collatz Prize winner Emmanuel Candès; Jean-Michel Bismut, member of the French Academy of Sciences; John Ball, member of the Royal Society, Former President of International Mathematical Union; Martin Groetschel, Foreign Member of the National Academy of Engineering, USA, the secretary of the International Mathematical Union; academician of the American Academy of Sciences Robert L. Bryant, Avner Friedman, Bin Yu; Yizhao Hou, member of the American Academy of Arts and Sciences and many more.

Since 2010, the lab has held annual academic conferences, wherein several influential mathematicians are invited to present their work alongside burgeoning young talents. Boasting attendance from both academics and students alike, these conferences not only excel at exhibiting knowledge from these outstanding mathematicians but also promote communication between the researchers from the School of Mathematics, and Beijing International Center for Mathematical Research, providing an environment from which new collaborations can arise.

The Key Laboratory of Mathematics and Its Applications consists of various outstanding scientists and has played an important role in scientific communication. Gongqing Zhang (Kung-Ching Chang), Boju Jiang, Shicheng Wang, etc. participated in the previous Mathematics and Culture Festival at Peking University and gave keynote lectures. Furthermore, many members of the laboratory also gave talks in different capacities to the benefit of many young people.