If you've wondered what topology was about and wanted to get a better feel for it than just a dictionary definition, then see the 20-minute video in the article

If you've wondered what topology was about and wanted to get a better feel for it than just a dictionary definition, then see the 20-minute video in the article. A blurb about the video: The computer animation "Outside In" explains the amazing discovery, made by Steve Smale in 1957, that a sphere can be turned inside out by means of smooth motions and self-intersections. Through a combination of dialogue and exposition accessible to anyone who has some interest in mathematics, "Outside In" builds up to the grand finale: Bill Thurston's ``corrugations'' method of turning the sphere inside out. Along the way, the narrators discuss the related case of closed curves and why they generally cannot be turned inside out. Everyday analogies such as train tracks, belts, smiles and frowns are used throughout, all richly animated and complete with sound effects. (quoted from http://www.geom.uiuc.edu/docs/outreach/oi/ http://www.geom.uiuc.edu/docs/outreach/oi/ )