Today, I got interested in the Erdos-Straus conjecture. See my comment there for details. Basically, I took a graphical/visual/geometric approach to a Diophantine equation. I've really got little to no experience with equations at that high a level; but the E-S conjecture was easy to visualize in terms of a unit circle. It's possible someone with better calculus and trigonometric knowledge than what little I possess could see some novel solution in my approach; I was just happy to devise an algorithm that provides more solutions than Fibonacci's. I coded the whole thing up in Python; I might upload it later.
Speaking of which, does anyone have experience with Google Code? I mean, can I just throw whatever I want up there and link to the source .py files for my programs? I've never used a revision control system like Subversion, but I'd like to learn about branches and trunks and so forth (beyond just saving my incremental .py files as 1a, 1b, 2a, etc.). I'd also just like to have my code available to me on teh internets so I can work on it anywhere without having to synch the laptop and my desktop.