Two things I found interesting about this story. One, Ms. Cairo is largely self-taught, including working through calculus via Khan's Academy. (I believe I predicted on this blog that we would see increasing numbers of young people who do things far beyond their years using only the Net for instruction. Not that that was a bold prediction, but this example suggests it is one worth looking forward to.)
And second, on the back of solving a "major math mystery" Ms. Cairo applied to ten graduate programs in math. She doesn't have an undergraduate degree or even a high school degree. Eight of the schools denied her admission, so she will start at one of the other two, the Univ. of Maryland, this fall.