P versus NP.
Hodge conjecture.
Riemann hypothesis.
Yang–Mills existence and mass gap.
Navier–Stokes existence and smoothness.
Birch and Swinnerton-Dyer conjecture.

Explanation:

The problem of P versus NP is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified can also be solved quickly. ... The class of questions for which an answer can be verified in polynomial time is called NP, which stands for "nondeterministic polynomial time". I don't know this answer, more to read about.

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