It's easy to distribute points evenly across a flat surface, but doing so over a curved surface is a much more complicated problem. Even spheres are hard. NPR's Scott Simon interviews mathematician Ed Saff who with colleague Doug Hardin has developed a new method of attacking this complex problem.

Press release from Vanderbilt University. You can also download the paper (in PDF form) from Dr. Saff's home page, if you think you're smart enough to understand it. (Don't ask me for help. I have two degrees in mathematics and was in over my head by halfway through page 2. I couldn't even make it out of the Introduction.)