(Euler's problem of buckling rod, with elastic linkages, bifurcation diagram. Its really a piece of art, inspiring awe as it looms in from infinity. I call it Pathological Menace)
My flavor profile for math is as follows and not in any particular order: Fractal Geometry, Non-Standard Analysis, Measure-Theory, Functional Calculus, Dynamical Systems, and Differential and Recurrence Equations.
For physics, I like Renormalization Theory, Quantum Mechanics, Quantum Field Theory, Path Integrals, and Meteorology.
This site has shown me that Abstract Mathematics is not for me. I much prefer Experimental Mathematics. More to the point, I like physics, but am not very good at it, relatively speaking, perhaps I'll get better with time...
If you've gotten to the bottom of this rant: I'll tell you what the most important concept in the entire universe is: Asymmetrical Balance.