Even if most of us will never understand such concepts, Raoof can teach us something else. Now a sophomore at Harvard University, she had planned to be a doctor even before entering the Intel ISEF. Well, her parents had planned for her to be a doctor, anyway. “I was born a doctor, even if I didn’t know it,” she says.

But her winning project gave her a new direction. Now she wants to get an MD and PhD and become a mathematical biologist. “If I hadn’t done that project,” Raoof says, “I would have always lacked the confidence about my ability to make some real contributions to math.”

Okay, now you can forget about mathematical knots. Here’s the really important part of Raoof’s story: Each year, there is a scientific competition that rewards the best and brightest kids, often with cash, and inspires them to challenge themselves in ways they might never have otherwise. And that kind of competition matters now more than ever because American kids can use a little inspiration and, yes, some cash motivation to improve in math and science.

Now, let’s talk about math. This time, it’ll be easy to understand. For the past several years, U.S. teenagers have been slipping in math and science compared with their international counterparts. In 2006, America’s 15-year-olds ranked behind those in 24 other developed nations in math, with Finland snagging the top spot. That is according to scores earned on a standardized test called the Program for International Student Assessment (PISA), which is given every three years to kids all over the world. American teens weren’t much better in science, either, ranking 21st out of 30 developed nations. (Finland came in first in this category as well.)

Experts have done plenty of pencil chewing to try to figure out why American kids seem to be losing their grasp on what was once believed to be a commanding lead in these subjects. There’s been plenty of blame passed around -- it’s Twitter’s fault or maybe TMZ’s. But talk to past winners of the Intel ISEF and you’ll hear solutions, not blame. And their solutions usually involve more competition.