The institute is "dedicated to increasing and disseminating mathematical knowledge." It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998 through the sponsorship of Boston businessman Landon T. Clay. Harvard mathematician Arthur Jaffe was the first president of CMI.
While the institute is best known for its Millennium Prize Problems, it carries out a wide range of activities, including a postdoctoralprogram (ten Clay Research Fellows are supported currently), conferences, workshops, and summer schools.
The institute is run according to a standard structure comprising a scientific advisory committee that decides on grant-awarding and research proposals, and a board of directors that oversees and approves the committee's decisions. As of January 2015, the board is made up of members of the Clay family, whereas the advisory committee is composed of leading authorities in mathematics, namely Sir Andrew Wiles, Michael Hopkins, Carlos Kenig, Andrei Okounkov, and Simon Donaldson. Nicholas Woodhouse is the current president of CMI.
The institute is best known for establishing the Millennium Prize Problems on May 24, 2000. These seven problems are considered by CMI to be "important classic questions that have resisted solution over the years." For each problem, the first person to solve it will be awarded $1,000,000 by the CMI. In announcing the prize, CMI drew a parallel to Hilbert's problems, which were proposed in 1900, and had a substantial impact on 20th century mathematics. Of the initial 23 Hilbert problems, most of which have been solved, only the Riemann hypothesis (formulated in 1859) is included in the seven Millennium Prize Problems.