Math Team

Great. So is your suggestion that high school students should focus on politics and building an equitable society instead of optimizing for themselves? That would be very altruistic indeed.

Solutions to linear differential equations are exponentials, and this may be what the author meant. In a state space model, we can write Newton's law under gravity if we let y(t) = [x(t), x'(t)]^T, let A = [ 0, 1; 0 0], let b = [0, -g]^T, and set y'(t) = A y(t) + b.

Indeed, the solution is y(t) = exp(A t) (y0 + int_0^t exp(-As) b ds).

In Einstein's theory, we have a generalization which says a stone's path through space-time follows a geodesic of the metric. In differential geometry, the exponential function, by definition, sends tangent vectors to geodesic curves.

So the author is right, under this interpretation.

> A mathlete is someone who participates in math competitions. He (almost always he)

That wasn't my experience. But FWIW I went to a public high school.

My friend (her) and I (he) both got accepted into an elite school, but we both had to go state colleges, because our families couldn't afford to send us. This was decades ago, when they didn't give out as many need-based grants.

There is a book called “Seven checkmarks” in Dutch that argues that succes in the Netherlands is strongly correlated to seven checkmarks to have: male, highly educated parents, white, certain type of elite high school, university educated and one more. Having all the marks, having generally underperformed academically and still coming out on top comparatively I feel there might be some truth in it. It would signal a quite stratified society with a “ruler class” inside a society that thinks of itself as classless for the last 60 years at least. (It’s pretty hard to reason about this being while being under scrutiny.)

Why post this? After reading your comment I thought wouldn’t want to live there or raise children there. But the second thought was, wait - that’s meritocracy in action. Imperfect meritocracy as you point out, but it might still be more equitable not than having seven checkmarks and generally faring worse than those born under a different star. My Rawlsian self thinks grit should be rewarded more than birth, even though testing for grit would probably massively increase burnout.

Thinking even further, I don’t think that societies with “high grit” (Korea, US) are generally considered to treat their children and general society very equitable. Still mentally debating if there is a very socialist argument growing inside of me. That book (read it three months ago) does make me think a lot. It was the first time something ‘near-woke’ made me think so hard. The book mentions the reflective point as well - might I only take it that seriously because it was written by someone from the same “class”? Foundational stuff.

This personal account resonated with me since I also had some personal experiences in both the "math competition" and "competitive high school" world up until I graduated high school in ~2018.

---

I went to a middle school where I somehow ended up far ahead in the curriculum due to my own interest in science and math, thanks to my personal interests and parental support at the time. I think I caught the attention of my math teachers and got to participate in a county-wide middle school math competition with some other students at my school. It was cool, and I wasn't, and still am not, a super competitive person, so I thought it was a fun experience to try; I don't think we won anything significant. I also think I took an AIME-style competition exam (sit-down test), but I don't remember much about it. All of this was cool but not super interesting to me at the time.

Some wise teacher or fellow parent at the time must have tipped off my parents about Math Circles, and I am incredibly grateful that my parents took me there. Math circles (at least in my experience) are like local meetups for younger (usually non-college) students to go and learn about cool exploratory and advanced (non-standard curriculum) math topics from college students and professors. I used to be so excited to go on Saturdays to math circles and sit and watch an old professor from a local college teach topics like logic, number theory, advanced geometry, and other math topics that were definitely not taught in my middle school. I also distinctly remember that I loved the exploratory side of the math circles as opposed to competitive math where I felt like I wouldn't learn anything and I had to get everything correct. If you have kids who are curious about math or even science, nature, and art, I would highly look into whether there are Math Circles in your local area and at least try it out. Some of my fondest memories during this time are from Math Circles.

I somehow ended up getting a full scholarship to attend a local (non-religious) private school with one of the top competitive high school math teams in the nation (among other extracurriculars like debate, model UN, ...). The summer school started there, and I won't forget when I went to the information sessions for the math competition team. The "vibe" was very off as soon as I walked in and not what I was expecting. The competitiveness was very evident in your attendance and performance in the multiple-times-a-week after-school math competition classes, how the best get to be on the A and B teams, and so on. I think I walked into it with the preconceived notion that I was going to get to learn more math for fun by joining the math team (like I did in math circles), but my naive worldview was very much shattered. I think I attended one of the local math competition events that first semester of high school and took one of the sit-down style tests, but there was no way I scored any kind of decent amount to be considered for anything related to math competition at that school. I also had one good close friend who stuck with math competition for the four years of high school, and so I got to get an idea of what that was like, and it was just as crazy as I thought it would be the whole time. I am actually grateful for him since I also got to talk to that friend about a lot of cool advanced math topics before I took those math classes, as well as help me learn enough of the math ahead of time to take the advanced AP physics classes (the electricity and magnetism one) that I had genuine interest in.

Luckily, by my second year, I was able to land on "science research" (think liek a really competitive science fair, e.g., ISEF) as a nice extracurricular I enjoyed. Even in that, you cannot escape the competitive nature of it, but there are alternative ways to branch out on your own (real publication, working with local colleges and professors, just being able to say I completed this cool research project and made this cool thing) and put something on your "college resume" without having to pigeonhole yourself into competing against other students all the time. I did have to cycle through some other extracurriculars (model UN and FRC robotics) where I "crashed and burned" before I finally landed on one where I would feel "safe" in a sense to enjoy what I was doing with research.

Finally, the big push from the school onto the students to get into the most prestigious schools they can get into really led to some weird dynamics among students and really unhealthy kinds of stress and anxiety to cope with. I think (but memories are fuzzy) that I was able to dodge a lot of that just by the nature of not being super competitive, but there were many students who would lose their minds if they didn't get above a 90% on an exam in an AP level class, as in genuinely freak out and stress over it and then go to the teacher and try to sort it out. Any grade that would jeopardize their perception of being smart or getting the highest GPA possible to get into the best schools possible was an anxiety and stress-inducing nightmare for them. There was very much an idea that "I'm not going to tell everyone else what I got on an exam" to also hide class rankings and your own GPA. I'm also sure that none of us got any healthy amount of sleep needed; there were people pushing insane courseloads with all AP classes to pad their "college resumes." I remember taking some architecture classes instead, which I found much more fulfilling and fun, and then feeling out of place trying to talk to some of my other classmates at the time who were trying to min-max their GPA and college applications.

---

Not to ramble on for too long, I just want to give an idea to some readers of another related personal perspective on this topic. Having been in some related environments in middle school and high school, I can really empathize with some of the genuine, agonizing, and sometimes lighthearted in hindsight, moments the author experienced. I can't imagine what it's like in 2023/2024, or even having kids in the future, what high school education will be like. Can students really find peace and comfort to just learn and pursue what interests them the most?

Quick epilogue: I did apply to all the prestigious schools that everyone else applied to (bless my parents for covering all the unnecessary application fees), but also thanks to my parents' pragmatism, I applied to some strong schools for engineering. I ended up down the Ph.D. route, and the exploratory open-endedness aspect of research is still what keeps me excited and happy in my day-to-day work.