PoincarĂ© Conjecture

The PoincarĂ© conjecture is a theorem about the characterization of the 3sphere, which is the hypersphere that bounds the unit ball in fourdimensional space. The conjecture states: Every simply connected, closed 3manifold is homeomorphic to the 3sphere. 
Millennium Problem
Solved

0 
P versus NP

The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified can also be solved quickly. 
Millennium Problem
Unsolved

2 
Riemann Hypothesis

The Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. 
Millennium Problem
Unsolved

1 