That conservation laws follow from deeper symmetry principles (Noether's theorem). Symmetry under translation corresponds to conservation of momentum, symmetry under rotation to conservation of angular momentum, symmetry in time to conservation of energy!
This has to do with the context where I learned Euler's Equation, but I can never separate it from Fourier and (later) Laplace transforms. Those are all so beautiful and mind blowing.
I'll second that Fourier transform. The idea that you could represent basically a list of numbers with a sum of sines, or any other orthonormal set is mindblowing to me. Nothing in math has blown my mind as much as functional analysis.
That conservation laws follow from deeper symmetry principles (Noether's theorem). Symmetry under translation corresponds to conservation of momentum, symmetry under rotation to conservation of angular momentum, symmetry in time to conservation of energy!
http://mathworld.wolfram.com/NoethersSymmetryTheorem.html