The “look for symmetries and conservation” edict is a direct emanation of Emily Noether's (First) Theorem, which basically places conserved quantities of a syst

The “look for symmetries and conservation” edict is a direct emanation of Emily Noether's (First) Theorem, which basically places conserved quantities of a system of differential equations with the symmetry groups that system must exhibit. A deep, amazing, beautiful, bi-directional relationship between differential dynamics and abstract group algebra.