"How Hard Is It to Untie a Knot?", by William Menasco and Lee Rudolph. American Scientist, January/February 1995, pages 38-49.
This article discusses a central problem in the branch of mathematics known as knot theory. Mathematically, a knot may be thought of as a closed curve with no loose ends dangling. The simplest example is a circle, known as the "unknot." A knot such as the trefoil knot---which has three over-and-under crossings---cannot be transformed into the unknot without cutting. However, if you cut the trefoil knot at one of its crossover points and reconnect it so that the string that was lying on the top is now on the bottom, you will be left with the unknot. The question the article explores is, What is the minimum number of times one must cut and reconnect a knot to turn it into the unknot? The authors show how this question is liked to deep questions in a branch of mathematics called topology, as well as to physics and DNA research.