\begin{definition}[Definition:Millennium Problems]
The '''Millennium problems''' are a collection of seven mathematical problems stated by the {{WP|Clay_Mathematics_Institute|Clay Mathematics Institute}} on $24$ May $2000$.
Each carries a prize of $\$1 \, 000 \, 000$ (US dollars).
Six of them remain unsolved.
They are as follows:
# P versus NP
# The Hodge Conjecture
# The Poincaré Conjecture (the only one of the seven to be solved)
# The Riemann Hypothesis
# Yang-Mills Existence and Mass Gap
# Navier-Stokes Existence and Smoothness
# The Birch and Swinnerton-Dyer Conjecture
\end{definition}