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Of the many puzzles mathematicians¹ ponder, one is new ways to tie knots. "There are more than six billion different types of knots that have been tabulated² by mathematicians. Six billion." David Leigh, a chemist at the University of Manchester in the U.K.

The hard part, he says, is actually making them. "Just because I can see a knitted jumper doesn't mean I can actually make one." Because what Leigh and his colleagues are interested in, is tying molecular³ knots—using strands⁴ that are 10,000 times thinner than a human hair.

"With a molecule⁵ you can't just grab hold of the ends and tie them like you would a shoelace. They're too small for that. Instead you've got to use chemistry to make the molecules⁶ fold themselves round into the precise way you need to form the knot."

Continuing the shoelace analogy—remember when you were learning to tie your shoes, your mom or dad put a finger in the middle of the knot, to make it easier to tie? Leigh and his team did something similar, but used metal ions as the "fingers" to keep the knot tying organized. Then tiny molecular strands, just 192 atoms long, assembled themselves around the ions.

"And then mum pulls her finger out—we extract the metal ions out—and you're left with just the knot at the end." The most complex molecular knot ever synthesized. The study is in the journal Science. [Jonathan J. Danon et al., Braiding a molecular knot with eight crossings]

Knots were hugely useful to our ancestors in the stone age: "fishing nets, axes with blades tied to the handles, how to weave fabrics⁷ to keep him warm." And Leigh says knots could be just as helpful in the molecular world—like for stronger braided polymers—maybe a better Kevlar.

After all, we do have six billion knots to choose from. "As every Boy Scout⁸ knows, different types of knots have different characteristics that make them more or less suited to particular tasks." And yes, Leigh himself was once a Scout. "I found knots difficult to tie then, and it hasn't gotten easier as I've gotten older."

—Christopher Intagliata

[The above text is a transcript⁹ of this podcast.]