Short answers, pulled from the story.
The seven complex mathematical problems were officially designated as Millennium Problems on the 24th of May 2000 during a ceremony at the Collège de France in Paris. John Tate and Michael Atiyah announced these challenges to an audience gathered in the amphithéâtre Marguerite de Navarre.
Grigori Perelman released his proof of the Poincaré conjecture in 2002 and 2013 after beginning work on it in the 1990s. He declined the Clay Institute's monetary prize awarded on the 18th of March 2010 because it was not also offered to Richard S. Hamilton.
Six Millennium Prize Problems remain unsolved despite numerous attempts by both amateur and professional mathematicians. These include the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier, Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, and Yang, Mills existence and mass gap.
The Clay Mathematics Institute pledged one million US dollars for the first correct solution to each problem. This event marked the formal selection of seven specific mathematical challenges including the Riemann hypothesis and the Poincaré conjecture.
Perelman refused the Fields Medal in 2006 and the monetary prize awarded on the 18th of March 2010 because he believed Richard S. Hamilton deserved equal recognition. Their work revolved around Hamilton's Ricci flow which is a complicated system of partial differential equations defined in the field of Riemannian geometry.