In this TED talk, Murray describes his opinion on elegant equations and how, in general, most equations can be simplified since the terms we need to describe them usually already exist. This relates to the concept of symmetry. Murray puts it as "an object or phenomenon exhibits a kind of symmetry if performing certain operations consistently on all parts leaves it description unchanged", and he demonstrated this with the example of how Newton described gravity as the force between two bodies, and years later Coulomb discovered the electric force between two charges, and the two were very similar in how they both dealt with the inverse square of the distance between the two objects. Murray also showed a slide of how equations were able to be simplified from a set of 8 equations to a set of 4 equations to a set of 2 equations, and this was possible using symmetrical relationships between the equations involving rotational symmetry and special relativity. This is, what I took it to mean, his meaning of beauty and elegance in science. How complex things may have complex equations, but can be simplified to simple and elegant ones.
I immediately thought of Albert Eintein's e=mc^2 equation when Murray mentioned elegant equations. It is a simple equation that describes a not-so simple principle in physics, and was only derived in the 20th century. And with that in mind, I can see what Murray is trying to say when elegant equations are more likely to be right than inelegant ones. There is less to work with, meaning that there's less room for error. So not only is it easier to understand and describe, but it is also easier to use and apply.
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