Contrary to what many believe, relativity and quantum mechanics are not considered to be the hardest concepts in physics. That distinction goes to turbulence, a flow characterized by chaotic property changes.
Heisenberg is reported to have said “When I meet God, I am going to ask him two questions: Why relativity? And why Turbulence ? I really believe he will have an answer for the first.” (wikipedia)
Turbulence is considered an unsolved problem in physics. (wikipedia)
Fields medalist Terry Tao explains why the core problem of turbulence is so hard (from a mathematical perspective). (html)