I too have a great fondness for Noether's First Theorem! However, just a slight technical correction: the theorem only goes one way. A conservation law alone do

I too have a great fondness for Noether's First Theorem! However, just a slight technical correction: the theorem only goes one way. A conservation law alone doesn't necessarily imply a (continuous) symmetry of the system. For example, there's no symmetry prescription for baryon or lepton number conservation. Of course, that doesn't bar them from arising from symmetries of some awesome future theory...