The Institute of Mathematics was established in 1947 in Kunming, China. The Institute's first director was Dr. Jiang Li Fu, with world renowned mathematician Dr. S.S. Chern serving as acting director in Shanghai. The Institute relocated to Taiwan in 1949, as research activities almost came to a standstill due to the difficulties caused by unstable political circumstances. When the situation improved a few years later, the Institute immediately began training younger talents. Within a few years, staff members of the Institute began pursuing research in many areas of pure and applied mathematics. When Dr. Y.S. Chow assumed the directorship in 1970, efforts were made to improve the funding of research as well as to extend research activities to include Probability and Statistics. Since 1978, under the directorship of Dr. Ky Fan, emphasis has been put on fundamental research (this being possible with the increase of research funding following the first Five-Year Plan of the Academia Sinica). Between 1984 and the conclusion of the third Five-year plan in 1996, research areas have been rapidly expanded under the directorship of Dr. Fon-Che Liu, Dr. Ko- Wei Lih, Dr. Chii-Ruey Hwang, Dr. Tai-Ping Liu, and Dr. Shun-Jen Cheng, to include many major areas of mathematics. At the same time, facilities have improved significantly during that period.

In December of 2009 the Institute of Mathematics moved to the newly completed Astronomy-Mathematics building located on the main campus of the National Taiwan University. The building is shared with the Institute of Astronomy and Astrophysics, the Departments of Mathematics and of Astronomy of the National Taiwan University, creating a center of intense mathematical activities in Taipei. Over the years, the Institute of Mathematics has continued to nurture mathematical talents in Taiwan through its extensive post-doc, research assistant, and summer school programs.