Why are particle physicists thinking about symmetry? Does symmetery make the mathematics less complicated?
Continuous symmetries are associated with conservation laws, which help understand and solve physics problems. For example, translational symmetry (i.e. nothing is changed in the system if you move the object from point x to point y) is related to the conservation of linear momentum in the direction of the vector from x to y. Another example is that if the system does not change as a function of time, that is related to the conservation of energy.