[agentultra]

Try building a computer from first principles[0]. You'll learn logic, circuits, systems programming, etc. Everything that runs our lives.

If you have a solid background in maths perhaps look into picking up a semester in some theoretical maths. You might develop a few hunches that could turn into innovative ideas when you return to your job.

Work on an open problem in maths with a small prize. See if you can crack it[1]. You could end up with a proof, some pocket change, and your name in the history books. At the least you'll learn what it takes to get there.

Pick up a few online courses or books on machine learning and dig through the Kepler data archive[2]. You'll learn statistics and modelling and perhaps confirm valuable research results! Space!

Go plant some trees. It's a small favor for the environment. It's hard work and you'll get really dirty. This is its own reward.

Volunteer in a foreign country. You'll meet new people and introduce yourself to problems you would never have considered in your lifetime.

[0] http://www.projectoberon.com/ [1] http://www.numberphile.com/videos/happy_ending.html [2] http://kepler.nasa.gov/Science/ForScientists/dataarchive/