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Math Trek

Unknotting knot theory

New techniques are beginning to unravel the mysteries of knots, revealing a great mathematical superstructure in the process

4:19pm, October 31, 2008

Sometimes, a simple, even childish question turns out to be connected to the deepest secrets of the universe. Here’s one: How many different ways can you tie your shoelaces?

Mathematicians have been puzzling over that question for a century or two, and the main thing they’ve discovered is that the question is really, really hard. In the last decade, though, they’ve developed some powerful new tools inspired by physics that have pried a few answers from the universe’s clutches. Even more exciting is that the new tools seem to be the tip of a much larger theory that mathematicians are just beginning to uncover. That larger mathematical theory, if it exists, may help crack some of the hardest mathematical questions there are, questions about the mathematical structure of the three- and four-dimensional space where we live.

One of the reasons knots have given mathematicians fits is that the same knot can appear in very different guises. Tug here, t

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