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"Square Knots" by Brian Hayes. American Scientist, November-December 1997, pages 506-510.
Mathematicians have always been fascinated by the under- and over-weavings of knots. A mathematical knot is a closed loop that may simply be a circle (called the "unknot") or that may cross under and over itself any number of times to form a knot that cannot be untied except by cutting the loop. An open question in this field of study is how to devise a method of determining when two knots are the same. This article describes a way of representing knots on a computer and discusses efforts to use these representations to answer mathematical questions about knots. These efforts show that the complex world of knots easily overwhelms computational attempts to catalogue them.
--- Allyn Jackson