characterizing a three-dimensional sphere would amount to settling the famous poincare conjecture, a 100-year-old challenge named for the great french mathematician henri poincare and chosen as one of the seven millennium problems. it now looks like the poincare conjecture has been settled by russian mathematician grigori perelman. in doing so, he may have provided the key to understanding what three-dimensional spaces look like, including the shape of our universe. the shape of our universe is a deep mystery, and jeffrey weeks is one of the mathematicians who's trying to figure this out. >> you go out into nature, you see the world, you look around, you want to understand what you're seeing. so it's like if you see little points of light in the sky, okay, you call them stars, but what are they? the same is true with the universe as a whole. i'm jeff weeks. i'm a mathematician. topology and geometry are my specialties. over the past 10 or 15 years, i've had the pleasure of applying geometry and topology to the study of the real universe to test whether our universe is infinite or fin