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 .
Ordinarily, when I think about a Math Phd student, I envision someone who’s known that they’ve wanted to do Math essentially their entire life. I think of a person homeschooled, who’s skipped on three grades in math, and won multiple math contests in the region. My friend would not have fallen into this category.
However despite lacking an intense Math background my friend had and still has a formidable work ethic. When she was in high school, she went to the library after school every single day, and would stay there working until it closed. On weekends when I’d occasionally go to get leisure reading from the library, I’d see her there working. After she went off the University of Pennslyvania, I was in the dark with her for about three years because she disabled all of her social media (e.g facebook). Given all of this, I’m not at all surprised that she excels as much as she does in Chemistry and Math. When you have a work ethic like that, double majoring into a Phd is really no big deal.
Mathematics resonates strongly with me because that was what I did and was good at in my academic life through high school. However, my story is a bit different from my friend’s. Unlike my friend (who immigrated from Korea) I was a prototypical Bay Area Math kid. I practiced supplemental material at home, skipped a grade in math and was an active member of the Math Contest Club through both middle and high school. I did reasonably well in math competitions.
Despite this, I never believed I was very good at Math. Part of this was because I spent my entire math career being overshadowed by my peer mathletes . How could I ever hope to pursue a future in math, when I wasn’t even close to a top mathlete in even my friend group? 
I gave up on math. Once I got to college, I stopped taking math classes entirely. I even went so far as to petition the Computer Science department to waive my Math requirement (due to the classes at Stanford I had taken while I was still in high school). To this day, my math ability is essentially where it was when I was in high school.
What I learned the hard way is something that I should have learned in Algebra class. Back then, the equation to know was slope y-intercept form, y=mx+b. We had perhaps an entire unit of doing nothing but understanding and graphing this equation. For all of the time I spent doing this, I never realized what this equation really meant.
The simple fact about life is that a little bit of extra slope can make up for a hell of a lot of y-intercept.
 I come from the Bay Area and there is a very strong emphasis in Math here. For example, my high school has several tracks for Math, problem-solving classes, and a very active Math Contest Club (a club in which I am proud to have been a part of).
In my friend’s case, I remember that the furthest math level that she reached in high school AB Calculus. She neither participated in math contests and did not do math outside of her school work. While I know that she did exceptionally well in her classes, it is with my Bay Area bias that I say she was undistinguished (at the time) in Math.
 I remember that while I was a student at Paly we had two kids make it to the MOSP International Olympiad preparatory camp in a single year. Consider that MOSP is for the top 40 mathematicians in all of the United States (It’s a boot camp for the International Math Olympiad). I knew the both of them personally and they are exceptionally well rounded individuals. In fact, one of them is one of my best friends.
(I often tell myself that I’m spoiled because I’ve been able to spend my entire life in the company of such highly intelligent individuals).
 It turns out that my close friend group was exceptionally intense - something I had no perspective at all about at the time. Even my close friends who don’t do math are intense about what they do. For example, I have a friend in high school who used to be All-American for swimming (which means he was one of the top 50 swimmers in the world). He once casually told me:
If I’m going to do it, I might as well try to best in the world at it.“
It makes me think of Nike. Imagine if Nike’s motto were changed from "Just do it” to “Just be best in the world at it”.