After all, beauty is the only criterion for a work of pure mathematics. People might use other words, such as elegant and interesting, and also, quite often, surprising to highlight different aspects of that beauty. And quite often, a math paper works in the way a mystery novel does (modern math papers, for silly reasons, are often written backwards and give away the name of the murdered on the first page -- and yet still work in the same way).
In the end, a mathematician would go in a certain direction because it is interesting, and the results will be appreciated if they are beautiful.
The article mentions equations, but quite often, equations are only there out of necessity. The ideas, often better expressed with diagrams, examples, and conversations might still need some algebra to be pinned down, but often enough, they are considered "ugly" and shoved under the rug. The mathematicians' word for this ugliness is technical; during the talks, they'll say somethings likes this:
>And so the limiting distribution of the number of sides in a single cell in a tesselation given by a geodesic curve on a hyperbolic manifold is given by a Poisson process. The proof is quite technical, so I'll skip it...
Which translates to the following:
>Here are two ideas that come from different worlds. It turns out that they are the same in this setting: like two lines in a poem that rhyme. The beauty of the poem is readily seen, but the rhyme is difficult to spell out with the alphabet of proofs and equations - so I will not do it.