Millenium prize problem

The Millennium prize problems are seven problems in mathematics where a  prize of $1,000,000 is given to the person who can solve one of them. So far only one problems has been solved: the Poincare conjecture. The Poincare conjecture is one of the most important question in the topology field.

Poincare conjecture:
   Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.

 Grigori Perelamn presented a proof of the conjecture in 3 papers. He was offered the prize money and a field medal to which he both declined, stating that it was not only him working on the problem; that people as far back as Hamilton has been working on and contributing to the proof of the conjecture. His proof was honored "Break through of the year".

The remaining Millenium prize problem are

1. P versus NP problem
2. Hodge conjecture
3. Riemann hypothesis
4. Yang–Mills existence and mass gap
5. Navier–Stokes existence and smoothness
6. Birch and Swinnerton-Dyer conjecture

Maybe you'll be the next to solve these famous problems

Unanswered Question:

1. How did the University, that propose these problems, know that these conjectures are true? Are they basing these conjectures on repeated observations?

Evaluation:
Complexity: 5
Interesting: 8
Quality: 7