Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation $a^{n} + b^{n} = c^{n}$ for any integer value of n greater than 2. 
Solved

0 
IMO 2009 Q6

Let $a_1, a_2, \ldots, a_n$ be distinct positive integers and let M be a set of $n1$ positive integers not containing $s = a_1 +a_2 +\ldots+a_n$. A grasshopper is to jump along the real axis, starting at the point 0 and making n jumps to the right with lengths $a_1, a_2, \ldots , a_n$ in some order. Prove that the order can be chosen in such a way that the grasshopper never lands on any point in M. 
Polymath Project
Solved

0 
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 