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American teens’ math and science scores are dismally low. Competitions like the Intel International Science and Engineering Fair may be the solution.

What you’re about to read may not be pleasant or intelligible. But it’s important, and it will be over quickly. So, let’s talk about knots.

These knots are not the kind you make with a shoelace. They are one-dimensional knots -- the kind you’d draw with a pencil. But not exactly. These particular knots, you see, exist not on a flat piece of paper but in a 3-D space. Think of it as the kind of space in which Jaws 3-D was filmed, only these knots aren’t as stupid as Jaws 3-D. Finally, these knots, like extension cords plugged into themselves, have no loose ends. (This sets them apart from Jaws 3-D, which had plenty of loose ends.)

Keep up; we’re almost done. Let’s summarize: one-dimensional, continuous loops floating in a 3-D space. What are they? They are what we call mathematical knots. Your brain probably hurts just thinking about that, doesn’t it? Now you and your aching head can comprehend how smart 19-year-old Sana Raoof must be. She won a $50,000 scholarship at the 2008 Intel International Science and Engineering Fair (Intel ISEF) -- the biggest competition of its kind in the world -- for her work on a project called Computation of the Alexander-Conway Polynomial on the Chord Diagrams of Singular Knots. Polynomials? Chord diagrams? Singular knots? Ouch.