An old high school friend of mine recently matriculated into the Stanford Phd program for Chemistry. We had a dinner celebration for her and I got to learn about all of the things she’s done since I last knew her in high school. To me, the most impressive of all of her feats is the fact that (in addition to Chemistry) she finished a second major in Math. In fact, she told me that she nearly pursued her Phd in Math. This personally impressed me because I used to know her when she was in high school. Back then, she was indistinguishable from an ordinary student math-wise .