The Clay Mathematics Institute (CMI) was founded in September, 1998 by Mr. Landon T. Clay, a Boston businessman, and his wife, Lavinia D. Clay. Their aim, as set forth in the Institute's mission statement, was "to increase and disseminate mathematical knowledge."

The first president of CMI was Professor Arthur M. Jaffe of Harvard University. The first Scientific Advisory board was composed of Alain Connes, Arthur Jaffe, Andrew Wiles, and Edward Witten. The current president is Jim Carlson, and the current Scientific Advisory Board is composed of Jim Carlson, Simon Donaldson, Gregory Margulis, Richard Melrose, Yum-Tong Siu, and Andrew Wiles.

The Institute has operated from offices in Cambridge, Massachusetts since its inception. In October 2002, CMI relocated to One Bow Street in Harvard Square.