Present math for non-mathematicians I am a graduate student in mathematics, and I recently got the question why there isn't a press release to the general public whenever we publish a paper (to advertise mathematics and increase interest).

Now, every paper is a bit extreme, but forced me to ask several questions:

Would arxiv be a good place to put math text aimed to the general public?
(I am currently trying to explain an article in a very metaphorical, but accessible to non-mathematicians).

Would it be considered strange to explain research for non-mathematicians either in a separate abstract in a paper, or also writing a shorter non-math version?
(I fear that this is considered slightly odd, 
and metaphors sometimes dumbs down the problem so that the question seems very silly. Also, will professors think it is a waste of time?).

A partial goal is to be able to explain what I've done the last five years to my family at the dissertation, but also get some experience in explaining math for grant applications. It would be nice if news from the world of mathematics appeared more often in the news, (local news for smaller achievements, explanations etc).
I would recommend blogging. This seems like the standard procedure for explaining your papers both to the lay audience and to other mathematicians (potentially ones that don't work on your specific problem). The blog format is preferable over arXiv or journal publications for reaching the lay audience because it is more accessible. Links to blogs are easier to share and faster to read than journals (which might be behind paywall!) or pdfs from arXiv. A blog setting also allows you to interact with your audience through the comments, this is the best way to help guide them through any confusion.

A blog setting can also be used to provide casual tours through proofs for experts and graduate students. This has recently started in TCS. Since this is aimed at the slightly technical audience, it is more appropriate to put on the ArXiv, although I would still advocate blogs.