[hessenwolf]

I regularly explain my PhD thesis on napkins. The explanation involves twins, one with a broken nose; fish; GPS satellites; and a tractor driving in a field.

Somehow this holds a crowd better than non-linear 72-dimensional space, and isometric and rigidity matrices.

[pcmonk]

But could they (1) extend your results or (2) have enough of an understanding of it to apply it to their work? The benefit of a napkin explanation is that they understand it well enough to know whether it would be useful/interesting to learn the issue better. If they really want to apply your results, though, then they'll need a better understanding. It's true that math papers aren't good for giving a surface-level intro to a subject, but they're not made for that. They're made so that if someone really wants to learn the subject, then they can.

[hessenwolf]

Very valid point. I suppose I just think we could make room in scientific papers, especially in the digital age, for an explanation of how the idea came about. I spent most of my early research career trying to find out how mathematicians got their ideas in the first place, because no amount of learning mathematics seemed to teach that.