Hi. Thanks for Yur comment.

In 2000 7 mathematical problems for XXI century were chosen. Making solution for any of them is paid by Clay Mathematics Institute. However, Russian Gregorij Perelman who solved one in 2003, decided not to take money.

Finding deterministic algorithm running in polynomial time for Hamilton cycle (or proving it does not exist) answers first problem, popular "P vs NP".

Here is more:
https://en.wikipedia.org/wiki/Millennium_Prize_Problems

If You will have more questions I will answer tomorrow.