That's very commendable. I am a nonmathematician who has become a mathematics teacher as part of figuring out why so few learners in the United States succeed in learning mathematics well. Here are some examples for you.

Good mathematicians (some Fields medalists) with readable blogs:

http://terrytao.wordpress.com/

http://gowers.wordpress.com/

http://www.arsmathematica.net/

http://www.scottaaronson.com/blog/

http://scientopia.org/blogs/goodmath/

http://wildaboutmath.com/

http://micromath.wordpress.com/

A list found by a Google search

http://www.onlinedegree.net/50-best-blogs-for-math-majors/

suggests more.

A few popular authors who are mathematicians write very approachable books about mathematics.

http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&...

http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&...

http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&...

Following links from links to the books by those authors will reveal other books by mathematicians who write for popular audiences.

Best wishes in gaining readers other than your mother (like me, for instance) as you communicate your interest in mathematics.

Mathematicians do have the advantage that all their papers are open-access. If you're interested in math, you can cruise on over to arXiv and read 60 abstracts an hour.

At most once. Links are what the internet is for:)

If you want links, here they are:

http://en.wikipedia.org/wiki/Field_(mathematics)#Definition_...

http://en.wikipedia.org/wiki/Cubic_field

http://en.wikipedia.org/wiki/Discriminant_of_an_algebraic_nu...

The thing is, those articles probably aren't brief enough for many people to stay interested, and they probably also don't go deep enough to make any particular one of impendia's results comprehensible. (And I'm also not sure if they're readable to people with only an engineering background in math.)

(In case you think I'm being snooty about engineers, I dropped out of college and have never published a theorem; instead, I have made my living writing software.)

But the OP's goal is simply to increase interest in his own work. Recurring concepts could be explained once somewhere and referred back to as needed, and the research and its implications could be elaborated on in far more detail than that given in the abstracts. This should not only be possible, but would likely be quite successful.

In my math classes, the engineers were the biggest whiners regarding mathematics. "I don't care about meanings, just tell me what function on my calculator to hit".

I've tried to read Terry Tao's blog; I like more advanced mathematics. His blog is very interesting, I'm sure, but the jargon level is so far beyond my knowledge it might as well be Russian for the level of meaning I draw from it.

Nerd Nite does the same thing, but with beer: nerdnite.com

Be a guest speaker at high schools in your area. Mike Merzenich graciously came to speak to my Neuroscience students, and they found it informative and inspiring.

Vi Hart does some really really neat math videos: http://vihart.com/

Above all, practice talking math to non-mathies. Use lots and lots of analogies, and don't forget to tap into the enthusiasm that brought you to the field in the first place.

It's nice if you can build a relationship between your institution and a school so you can have a sort of standing gig every few years.

(Also note that some schools will totally love this and others might be unresponsive, so don't give up if the first one doesn't happen)

The kind of progress where an engineer or scientist takes what they need from that obviously useless piece of mathematics becomes harder and harder as the silos get deeper. But things are getting better. Stuff like mathoverflow, blogs by researchers, polymath are really helping bridge those gaps. Thats why these days people are really starting to see all this stuff that we thought unrelated are actually just different aspects of the same thing. I especially like whats going on with category theory, information theory, information geometry, entropy and bayesianism. Together they leave no subject untouched. Not one.

First of all, my interest is not so much to increase interest in my own work. My work is pretty modest compared to the likes of Tao and Gowers, so really I would be happy just to represent the mathematical community and discuss the field I work in as a whole.

I think kragen's comments are essentially correct. I could do a good job of explaining what I do, and why it is interesting, to someone with an engineering background in about five to ten pages. IMHO that is a lot of effort required to either write or read. Of course my impression of HN is that there are indeed people who would not begrudge the effort to read it!

The suggestions have revolved around blogging. I confess that I don't have so much of a taste for this -- I spend a lot of time at a computer as it is, and there are already outstanding math blogs online as pointed out by tokenadult. I would be much more excited to do something that involved face-to-face talk. So perhaps my request is more difficult than the initial impression I gave!

Thanks to all.

I don't think that means the work is unimportant, but I think of math as being primarily a recreation like painting or singing, and only secondarily something that needs to be of service or interest to others.