A grounded person would get a science tat like Ohm's law. Personally, I don't care about the real world. Get the fundemental theorem of finitely generated abelian groups. Or if you like Rs more than Zs, the analogous result for decomposition of R-modules.

My wife and I spent two years in South Africa in the Peace Corps as education volunteers at rural schools. I had a BA in mathematics and she in journalism. IMO: 1) In poor areas, volunteering technical skills is a long term commitment. However, many rural schools all over the world need new outdoor bathrooms. If you go to a place like this, find a Peace Corps office and they can help contact a Volunteer that would be happy to have you help out with anything for a week or whatever. They will know more about the area than you will ever learn in a week or two and can share good info. 2) Southern Africa is a great place to visit for something like this. Getting there is a little expensive, but everything else is like half-price once you get out of the major cities. Also, there are trustworthy car-rentals and it is relatively safe outside of the big cities despite what people believe.