[pcmonk]

I loath academic papers. Often I find I spend days or weeks deciphering mathematics in compsci papers only to find the underlying concept is intuitive and plain, but you're forced to learn it bottom up, constructing the authors original genius from the cryptic scrawlings they left in their paper... and you realise a couple of block diagrams and a few short paragraphs could have made the process a lot less frustrating.

It's like this all the time in math papers. It often seems in the end like the ideas themselves are fairly straightforward, and it shouldn't have taken that long to understand. I think, though, that if you actually sat down and tried to explain it in more intuitive terms, you'd find that you might not be able to. True, you could find a way to convey the general idea, but without the technical details, (1) while non-mathematicians may get a surface-level understanding faster, even mathematicians will not grasp the technical aspects, and (2) it will be very hard for anyone to extend your work or for anyone to apply it to another situation, so it will only be applied in the specific contexts that you explained it in.

Language isn't built to communicate math, so doing so effectively will be either difficult to understand or imprecise. Many people claim that it would be easy to explain deep math concepts with "a couple of block diagrams and a few short paragraphs"s, but I'd challenge them to write a textbook on abstract algebra, or topology, or something like that before they make that claim.

[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.