Unfortunately there isn't a single publication that does justice to what I've pieced together. By that I mean, because I had such a poor understanding of math, every little bit of knowledge and intuition that most people learn implicitly, I had to learn explicitly. The downside is that it took me all this time to realize how useful math is, but the upside is that I now have created several explanations (both in text and video format) where I explain all of these intuitions in a piecemeal way, slowly building up a model of the world, but without any math notation and without ever talking about numbers, just objects in general and relationships between them. You can go from scratch (things you see around you) all the way to category theory without realizing you got there, all without notation, just building intuitions. That's what I do in the videos, I use the idea of a caveman looking around and starting to discover these relationships, and building on top of them.

I must have more than 15 hours of material that I recorded as I was piecing together what I was (and am) learning. I should put them online - I haven't done it yet because I think it drags on for too long, but maybe I should put up one or two and judge from the comments and go from there.

Mostly I gathered these ideas by first finding out that Set Theory is at the beginning of math. Then I found out how categories and types and sets are all equivalent. Then I read some papers that explained that and for that they needed to step back and give some intuition of each and how they relate to each other. I explored so many links, but the knowledge is scattered.

I will publish some of the stuff I made, now that I know there's interest, when I'm back home on Monday. If you want to know about it, send me an email (it's in my profile page) and I'll let you know.

Publish it. Don't get caught up in perfectionism. This would be highly valued by me and many others even if it does "drag on" at times or lacks polish in certain areas. You have just recently bridged a gap that many would like to bridge, so it is still fresh in your mind what it is like to be on both sides of that gap. It's that freshness that lends unique value to your material. A 20 year professor might be an expert, but she has lost that freshness.

So publish it! Please!

Seconding this. Publish it, even if its a mess. Just make it CC, other people will clean it up if they think it's worth doing. If they don't, no loss to you.

As somebody who is looking for engaging ways to teach my young children math, I will also ask you to please please make this available. (And I can fully agree with previous comments regarding perfectionism and creative commons).

Wow, thanks for the interest :) I will definitely publish it this weekend on Youtube (I'm not home right now so I don't have access to the files). If you'd like to be notified about it, ping me on my email; I would love to have feedback on them!

If you are interested in math in relation with programming, I really like blog at http://jeremykun.com

If you feel your math is too rusty to follow along, http://jeremykun.com/primers/ should get you started, and then just choose the topic in http://jeremykun.com/main-content/ ... or maybe the other way around :)

Mathematics for non-mathematicians, Foundations of Arithmetic were the books that did it for me. Amazing books.