This years Abel Prize, sort of a Nobel for math, has been awarded to an Indian mathematician by the name of Srinivasa. If the implications of this don't mean anything to you, let me give you the history. (Or you can find a quick reference to it in Good Will Hunting.) In the early years of last century, a British mathematician began receiving notebooks in the mail. They were filled with page after page of scribbles proofs. Many of them were unorthodox versions of known work, but some were intriguingly new. They turned out to be from a young Indian named Srinivasa Ramanujan. The boy had taught himself math using a primer he had found, and with nothing more than that was able to create entirely new lines of math. He is best known for his work with continued fractions, but perhaps his greatest legacy is the one that inspires young mathematicians the world over. It is possible to come from nothing, from the middle of nowhere, and yet solve puzzles that have confounded the great minds for centuries.
Problems like P vs. NP, commonly epitomized by the Traveling Salesman Problem, may just take a really good idea from a fresh mind. That simple possibility is what keeps math new and exciting (for those of us who care enough anyway.)