[1] While the institute is best known for its Millennium Prize Problems, it carries out a wide range of activities, including conferences, workshops, summer schools, and a postdoctoral program supporting Clay Research Fellows.

As of September 2024[update], the board is made up of members of the Clay family, whereas the scientific advisory committee is composed of Simon Donaldson, Michael Hopkins, Andrei Okounkov, Gigliola Staffilani, Andrew Wiles, and Martin R. Bridson.

The conference will be accompanied by workshops from September 30 to October 4, 2024. Notable workshops include: Daniel Graham from the University of Surrey won the Gold Medal for Mathematical Sciences at the 2024 STEM for Britain competition for his work on quantum authentication methods.

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.

Its recipients to date are Ian Agol, Manindra Agrawal, Yves Benoist, Manjul Bhargava, Tristan Buckmaster, Danny Calegari, Alain Connes, Nils Dencker, Alex Eskin, David Gabai, Ben Green, Mark Gross, Larry Guth, Christopher Hacon, Richard S. Hamilton, Michael Harris, Philip Isett, Jeremy Kahn, Nets Katz, Laurent Lafforgue, Gérard Laumon, Aleksandr Logunov, Eugenia Malinnikova, Vladimir Markovic, James McKernan, Jason Miller, Maryam Mirzakhani, Ngô Bảo Châu, Rahul Pandharipande, Jonathan Pila, Jean-François Quint, Peter Scholze, Oded Schramm, Scott Sheffield, Bernd Siebert, Stanislav Smirnov, Terence Tao, Clifford Taubes, Richard Taylor, Maryna Viazovska, Vlad Vicol, Claire Voisin, Jean-Loup Waldspurger, Andrew Wiles, Geordie Williamson, Edward Witten and Wei Zhang.