There are all different kinds of measures of elegance in science and mathematics – the shortest proof, the most all-encompassing theory, the equation that best fits the data, and so on. But there is another kind of elegance entirely, which is concerned with non-mathematicians and non-scientists – people outside the field.

To whit: What is the scientific or mathematical theory that best converts a subject which had formerly been arcane, obscure, approachable only by the well-prepared priesthood, into something that is understandable by anybody, with only the simplest of explanations.

This property of a theory might be called its “Popular elegance”.

My vote for the theory that most possesses this propery is the Feynman diagram. I can’t think of anything else that caused a subject so arcane, in one fell swoop, to become so much more clear.

Can anyone else think of worthy candidates?

very good recommendation. a few additional examples come to my mind:

* the Bohr Model

* the Traveling Salesman Problem

* the Schrodinger’s Cat Paradox

* Zeno’s Paradox re: Achilles and the Tortoise

it is likely the case that the Bohr Model most closely fits your description of an explanatory theory; however, I include the two paradoxes as well, due to their classic and historic role in providing a simple explanation or insight into very complex scientific and mathematical problems.

I would definitely say the halting problem, to popularize theoretical computation.