Untangling a knot may seem simple, but the theory of knots has tied up mathematicians for decades. Now, mathematicians Joel Hass, of the University of California, Davis, and Jeffrey Lagarias of AT&T Research have proved an important point. They have shown that when a simple loop of string is tangled up, it is always possible to untangle it in a limited number of steps. Mathematicians group knots into types, depending on how many times the loops cross each other. The simplest kind of knot is a closed loop. Mathematicians call this a trivial knot, or unknot. "Imagine a garden hose, with the ends joined together to make a loop. Then if you tangle the hose up, it can be pretty hard to get it back to the loop," said Hass. What mathematicians did not know was the maximum number of moves it would take to turn a tangled loop of hose back into a plain circular loop. Hass and Lagarias have now found this number, although it is enormously high. The result should spur other mathematicians to find ways to reduce this number, said Hass. Knot theory is connected to many other fields, said Hass. For example, every cell in the human body contains over a yard of DNA, which is coiled and tangled up. Knot theory can explain how DNA untangles itself to allow genes to be read, said Hass. The paper is published in the Journal of the American Mathematical Society.