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"Loopy Solution Brings Infinite Relief," by Charles Seife. Science, 9February 2001.
How long does it take to untangle a tangle? Mathematicians have been studyingthis question for years in the field of knot theory, with no definitive answer.Lately there has been a step in the right direction---Jeffrey Lagarias of AT&Tand Joel Hass of the University of California, Davis have proved that onlyfinitely many moves are required to untangle the simplest knot of all, a loopof string called the unknot. While the bound on the number of moves isridiculously large, the proof of the existence of this limit is inspiringfurther research.
--- Benjamin Stein