Math Team
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benexdict.io
Yes, there are many students (even more these days) that are in the grind for the accolades and college admissions, but math competitions were genuinely my favorite part of high school. They helped hone my problem solving, grit (!), work ethic, social skills, and leadership skills in a way that I continue to see pay off 15 years later. I am forever grateful for my high school teacher who supported me during this time.
It helped that I was actually passionate about it, which I think is the underlying point here. Weird constructs like math competitions that help kids channel their passions? Incredible. Forced hoop-jumping for the purpose of college admissions? Horrible.
> Nights were for other worthless extracurriculars to pad out our applications. ... The worst part was knowing that it was all going to be extruded into a few lines in an application form, that a committee would review for about ninety seconds
This is the tail wagging the dog; work really hard for 4 years in HS so that the next 4 years will be spent at a comparatively more prestigious college. I don't think we should expect high school students to be able to optimize this correctly themselves, and from my experience guidance counselors weren't particularly helpful. College admissions feel like a local maxima that have a lot of unintended side effects but would be difficult to change.
Personally, I didn't do the extracurriculars that would look good for college, but rather the ones I enjoyed; I didn't study very hard either. Didn't get into Stanford or an Ivy, but I look upon my experience in high school/college fondly rather than bitterly. Life seems to have turned out ok too.
It's also interesting to follow the trajectories of people who were in the group that over-optimized for outcomes but have fallen off that path. I think the author was able to mitigate his burnout (I presume he had a good tech career), but I know a fair amount of folks with good pedigrees who haven't, and are still in limbo (unemployed, underemployed, or taking an extended break early in their career/schooling). I know they have the potential to do great things, but it seems the stakes of burnout are much higher today and harder to recover from financially.
Among S, T, E, and M, only the last one doesn’t get fun toys to play with.
My major takeaway from his article was "The things we do in the high-stakes holistic admissions structure we've set up are insane" more than anything to do with competition math in specific.
My former team is still alive and going strong, and after uni I went back as a coach. I still hear the same stories about how awesome the group is, and how kids that now are in the same position as I was find it a "safe space", if you will.
I wasn't great at it, but I was pretty good considering that I didn't get any training, and I always thought it would have felt amazing to actually get good at those tests and feel like a math wizard. I guess I'm a bit bitter about it; it's a shame the special opportunities go to people who are depressingly minmaxing instead of people who would really love to have them. Although I also know that at some level if I had 'resolved' to get good I could have, so I can't be too resentful.
...but its actually an interesting (and not super difficult) exercise in its own right to figure this out even if you don't know the formula. Encourage you all to give it a shot.
SPOILERS: 9999 = 3^2 * 11 * 101, so first subtract out the multiples of 3 (3333 of them), the multiples of 11 (909 of them), the multiples of 101 (99 of them). Note that we've now double-subtracted multiples of 33 (303 of them), multiples of 303 (33 of them), multiples of 1111 (9 of them) so add these back. Finally subtract 1 to not count 9999 itself.
phi(9999) = 9999 - 3333 - 909 - 101 + 33 + 303 + 9 - 1 = 6000
I guess my point is that the purpose of these problems is not to separate out people who know specific tricks from people who don't—its to separate out people who can reason their way through difficult mathematical problems and people who can't.
Trying to come up with everything from scratch could take a lot longer and be very frustrating when you've got other problems waiting for you to solve.
If that is frustrating instead of thrilling to you then you probably shouldn't do these competitions.
I think I can understand why the author complains about drilling for math contests. I think it’s the same reason high level chess players complain about opening book. Drilling is not fun and it reduces the creative element of solving the actual problems.
The fact that he wasn’t doing it for fun but for college admissions plays a lot into it as well. That kinda pressure can really kill the fun.
OP says in the article that he didn't understand what he was doing, but was just trying to imitate people who did to try to appear brilliant. And he claimed that most students in club were like this, due to parenting and teaching that was focused on resume building for ignorant Admissions Offices, instead of focused on learning.
It really isn’t. The essay makes this point as well. The acquaintance of his who was most interested in math dropped out of the contest team. He went on to become a mathematician because he was actually interested in understanding higher math and how things fit together.
Drilling is just practicing computational tricks to be able to execute them by heart. This would be true regardless of the amount of time pressure or lack thereof. I’ve taken many math courses that had exams in this style and I always hated them. I much prefer trying to figure out a proof I’d never seen before. For any real work, those computations would be done by a computer anyway.
LeBron James much prefers to slam dunks, but he still has to practice the game ad condition.
https://artofproblemsolving.com/wiki/index.php/2022_AIME_I_P...
The totient formula isn't the hard part of the problem.
The test has a very short time limit (for the difficulty of the problems), and has many gruelingly complicated problems,so if you dont have the formulas down cold, you'll burn out during the contest.
Of course, if you don't care about silly speed-mathing contests, you can enjot the problems at a leisurely pace.
* The contest has 15 problems and a time limit of 3 hours, giving only an average of 12 minutes per problem.
* The average score is 4.83/15, from the official statistics [1].
* The statistics noted that only 5.17% of test takers answered this problem correctly, making it the second-hardest problem out of the 15 on the exam.
[1] "AIME 02/08/2022" https://amc-reg.maa.org/reports/generalreports.aspx
OP missing this point shows that he really was doing this for all the wrong reasons. He should have done FIRST or science bowl instead.
Asking for N mod 1000 was another cute twist that was meant to get you thinking about the divisibility properties of the totient function - "hmm, so (p-1) always divides \phi(n) for all prime factors p of n, how convenient..."
For every distinct prime factor p (so, of 9 is a factor, use 3 not 9), only (p-1)/p of the natural numbers ≤ n are relatively prime to it. Pime. This overcpunts nothing, since prime factors are relatively prime to each other. (Proving this requires some analysis of remaimders / modular arithmetic. But working an example shows the pattern).
This gives a formula, phi(n = Sum (p_i ^ e^i)) = n • Product ((p_i -1)/p))
This also shows how OP (and maybe the coach) missed the point of math team.
There are a huge number of kids in this authors shoes, ones who are on a treadmill and not entirely sure why. There are also lots of kids who were always the best at something (in this case math) that any of their teachers etc. had ever seen ... until they move across the country and find themselves in a classroom where they are middling at best. And sure, there are rare kids who are so good it catches you off guard.
FWIW I suspect there are more kids made miserable than those who thrive, but I think it's largely unavoidable in a tournament system like "elite" college apps. There are also plenty of kids who had some fun and made some friends along the way without taking it too seriously. I suspect in this case it's often a good outlook in high school, especially for kids who don't really fit in anywhere else.
There were rumblings that my high school, which had plenty of AP classes already, was about to introduce a combination AP/IB curriculum, which absolutely terrified us. I and my AP-taking classmates breathed a huge sigh of relief when it was announced that it would be delayed, and the students in the year below us would be the guinea pigs. They would have to run twice as fast just to stay in place.
The best part: Even a decade ago, the above was considered neccesary but not sufficient for admission to a top school. Plenty of people with perfect to near-perfect college entrance exams, Intel International Science and Engineering Fair finalists, etc didn't make the cut. Of the few that did, the majority were the lower Ivy's (Dartmouth and Brown).
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.
BTW MIT doesn’t do legacies.
I think a lot about a meme I saw: "I'm a therapist, and while therapy is great, what I think what most people need is money."
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.
Huh?
You can say “state space,” invoke the general solution to inhomogeneous ODEs, and write it out with integrals and matrix exponentials, and the answer is still quadratic. Unless you consider t^n e^(0t) to be exponential. (Hint: what are the eigenvalues of A? One could start by calculating A^2.)
Which leads to one of the most important lessons from all of physics: you can take a problem, use a different technique to solve it, and you get the same answer! It’s magic.
Maybe you would personally say that neither of these cases is truly or essentially exponential, since we have more recognizable closed forms. But then you should also commit to saying exp(it) = cos(t) + i sin(t) is not truly exponential. I would find that a little strange, but to each his own.
Anyway, I agree that you get the same answer in the end, as you must.
My experience with doing competitive math and programming stuff was generally quite enjoyable even though I never did the best or made it to an ivy league school. I'd still encourage any kid who's at all interested to try them out. Solving puzzles is fun! Who cares if learning number theory is "useless". So are video games, football and chess.
My experience is similar to you - I too really enjoyed my time doing these activities but once everything I ever enjoyed started becoming brownie points for my college applications, the competition started becoming "Grind X tasks and Y patterns so you can make the grade! Cause if you don't solve this in 14 minutes, then that kid will and he'll get your position!"
Of course, some places are working on genuinely hard problems. They need outstanding individuals, and these are what elite schools offer: They've already done the filtering, ensuring that the very highest performing individuals disproportionately possess one of their diplomas. The elite school may or may not have the greatest instructors, but regardless the students will get a superior education simply due to the fact that they are embedded in an environment that surrounds them with outstanding talent.
In this way what university you went to acts a signifier as to your abilities, not just how much you know, but how rapidly you're able to learn new things, and how much work you're willing to put in.
On one side, it is probably good to motivate pupils to aim for something, and get good at it - but on the other side, you obviously end up with a bunch of kids that are just really good at grinding away - even if their heart is not there. And must become some obligatory thing, because everyone else is doing it.
FWIW, over here academics is the only thing that maters. There are no entrance exams, no personal letter, no letter of recommendation, no extracurricular activities. Your GPA is the only thing that maters.
(Of course, that also has its downsides. People end up re-taking HS exams year after year, because someone beat their GPA with a decimal point.)
One factor could be that, AFAIU, schools in US have many more electives than in Europe. As a student you have the choice to take more advanced classes for one subject, and only basic in other subjects, whereas in Europe, the curriculum is standard for all. So Universities in US need to compare performance on different axes.
> Of course, that also has its downsides. People end up re-taking HS exams year after year, because someone beat their GPA with a decimal point.
Another downside to the one-size-fits-all standard curriculum, is that it forces you to care about classes that you don't really care about, while not being able to focus on the subjects that you're really interested in. I think in US, if you're really good at something, universities may ignore average-to-poor performance in other areas.
With that said, we have around 20 universities and colleges in Norway, versus the thousands you have in the US - so I would imagine that elite employers in the US rely more on colleges/universities for the filtering part, which in turn filter HS students. A whole lotta filtering going on, it would seem.
My 17 year old son is in the Irish system. Top 6 subjects count for points, nothing else. Plus some minor need to pass requirements on other subjects. i.e. you cannot just specialise in science and maths at the end. (His 6th best subject will be Irish, English or French, all hard to get very top marks in.)
With dumbing down/grade inflation the skill to get ahead into a good degree is be pretty good at everything. Rather than absolutely brilliant at a couple of things.
He did a tiny bit of computers and maths extra classes, but we could not keep the maths classes going when it went back to in person after COVID, as we are on the poorer side of Dublin. Small chance he goes to Britain for undergraduate, which will be weird as he would suddenly have interviews/CV/Resume, whereas no interview/CV/Resume in Ireland.
I wonder if part of the difference is that universities here in the UK aren't too worried by extracurriculars, especially for maths and science subjects.
I don't think my participation in contests was a factor in getting a place at Oxford - only the exams and to a lesser extent the interviews were. There's a short section on your general university application form where you write about such things, but unless you write something totally daft, it's general not a big factor. I interviewed people applying to Oxford for maths one year, and we really didn't pay any attention to the candidates' 'personal statements', although if any had been remarkable I guess we might have noticed. My mother was the maths admissions tutor at Imperial for years, and again they really didn't worry too much either - they cared about A-level grades mostly.
for me, it was debate club. i liked debate, but the form of it i participated in was a rich man's game and i was simply not a rich man. i didn't have the money to fly to the east coast every weekend to attend tournaments or pay people to assemble cases and evidence briefs for me. it wasn't worth the coaches' time to even listen to me practice because i wasn't wealthy enough to compete at a high level.
that feeling of futility persisted across other extracurriculars. i participated in the science fair, but my advisor instantly became dismissive when it became clear that my parents couldn't gift me a competitive research opportunity at their lab or hospital because they, y'know, didn't work at a lab or hospital. the school i went to had a lot of rich kids; i once spotted one of my classmates at the airport on their way to volunteer in uganda over the summer.
math team ended up my saving grace. perhaps it's because we weren't quite so competitive - we did well regionally but were not competitive at a state or national level - but there was something freeing in just solving math problems. afterschool math practice was free and open to everyone. there were a variety of different competitions, team and individual, geared for different skill levels and specializations. no one cared about what my parents did for a living, thank god. it was just about solving the damn math problem.
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.
I'm more interested in this "Analysis II" the author mentions taking in his freshman year. "Analysis II" at the undergraduate level usually refers to a proof-based course on real-valued functions of several variables. Basically, a retread of Calculus III with a more rigorous foundation. But the author never mentions any mathematical results from calculus and beyond, and I'm under the impression that grade-school math competitions only target subjects in arithmetic, elementary combinatorics, and classical geometry.
It seems quite unlikely the author was referring to Real Analysis! Still I can't find nearly any reference to high school Analysis (except https://calcworkshop.com/math-analysis/), so I'm guessing that terminology is nearly gone now.
Meanwhile, Harvard calls its honors Real Analysis class "Advanced Calculus".
But on this case it's precalculus. International Baccalaureate also uses "Analysis" to mean precalculus mathematics.
Personally, I just liked solving all sorts of puzzles and math problems and other sorts of contests. There's nothing like the adrenaline rush of competing against other people in a mental challenge under time pressure. I had some books with math problems, and I liked reading those, and I did well in the contests, and that's all it really takes. You don't need a team. But I enjoyed it.
Obviously if you like competing in math contests and you are good at it then it's a good thing to do. I'm not sure how good of an idea it is to "force it" and try to get good at something that you really aren't that into.
If you're a smart person, there must be something intellectual you can really get into, right? Hopefully?
Now that he's 15 years into a tech career, I'm wondering what he thinks if/when interviewing applicants, and sees or doesn't see similar grind on the resume.
I imagine that some, if they got their position by virtue of the hoop-jumping grind, would think that the grind was positive signal for a candidate for that kind of position. But I don't know how common that belief is.
Reason I'm wondering... The last time I did a call with a FAANG recruiter (for Staff/Principal SWE), they did something new, running down a long list of checkboxes, and asking me for each one whether I had it or not. Most of it sounded like college application fodder, like people get coached to do in affluent prep schools, including multiple checkboxes about mathlete competitions. Not something that I would've thought would still matter for someone with a big industry track record. Was gathering this college app grind data for experienced candidates a new thing, or have recruiters and resume-scanning software been filling out these properties of each candidate for a long time?
Then transferring that innate problem solving drive and aiming it towards the problems and challenges facing the company.
How do you know you can aim that person's drive for math towards company problems?
Unless and until you know that, is it more positive signal to look for people who, well, have solved company problems?
After hiring couple of those people I've become quite vary of them.
In general, it was pretty low key. Local meets were every month or so, practice was about 2 hours a week, though we did more for states. At no point did I think about the impact on my college admissions, and I don't recall it coming up in conversation with anyone else.
(warning: humblenrag) In fact, the only real negative memory I have was that the individual high scorers got graphing calculators until the year I had the high score and got a calculus textbook. Of course, when I got to college and had to pay for textbooks, I learned that the calculus text probably was more expensive than the calculator.
Quiz Bowl was full of a ton of smart kids with various interests. We "practiced," but the only skill you could really develop was being able to predict a question before it was finished so you could be the first to answer. Questions varied widely from competition to competition. One time we got to be on local TV to compete, but there really wasn't a season or tournaments. It was mostly 1 on 1 matches after school. Overall it was a ton of fun.
Academic Super Bowl was also full of smart kids, but they were more goal oriented. It was something you had to study for. Before the competition you were given some categories, you assigned categories to teammates, studied, and then competed at various events. It was literally just more memorization. I got drafted to do it one year the night before a competition, because I was The Guy for a topic they needed a teammate for. It was awful. I fumbled my way through because I didn't have near the detailed knowledge required for the specific subcategory. I probably would have done better if I had more time to prep. It was a big tournaments, and at the end there were different prizes for schools by various sizes.
The type of kids in the two were varied. Everyone wanted to get into a good college. The former seemed to love knowledge for the sake of knowledge. While the later had a ton more grit, they lacked passion in areas outside of directed study. The former would read a book, because it was mentioned offhand in another piece of media. The later would read a book because it was assigned to them.
Reading through this thread, it seems like people's experiences of Math Competitions varies from one to the other. Having grit to study and work at it gets you far, but having passion probably gets you further. The issue is grit tends to be fungible while passion is not.
I've got a freshman in high school - and he's very bright - doing AP Calc now. But he already feels like it's impossible to get into these schools so why bother. He started the conversation tonight with "I don't think I want to go to MIT anymore." Which broke my heart a little bit - not because I care whether he goes to MIT - but because it you could see his expectations being crushed by reality.
This is the system that we have built for higher education in the United States, and it's incredibly f*cked up.
I think it was less painful pre-internet, pre-globalization, where you only had to be the best in your town, or your state, and that was pretty dang impressive. Now if you aren’t the best in the world what even are you?
Regarding your kid: There are 4million US high school graduates each year. MIT admits about 2000.
Sorry for being abrasive, but why is your child crushed that he isn't the very best? Why is it sad that he isn't better than everyone else?
Being upset about not being in the 0.1% as a teenager is tacky. 99.9% of us aren't.
Although the playing ground was actually fair and hard work gets you on even footing, I have a couple of things to say about college admissions. I will definitely say that although the top universities claim to be meritocratic, I don't think they are. Most of these students, maybe all now, are kind of acculturated into this college admissions process where from a young age you are doing STEM competitions and building letters of rec. A lot of these kids have parents who move the whole family to be near to a high school that can get their children into the top schools. Most people in the US are not aware, or unable to do anything with this specific cultural knowledge you need to get in to those schools. Exceptions do not make the rule. So the top schools are filled with people who don't reflect the country which is bad I think.
Second, as people have focused on STEM accomplishments just to get in to the top schools, I think Goodhart's Law is in action and that STEM competitions and precocious authorship is becoming less meaningful but whether admissions offices change I don't know if that will happen and has not yet. So these will continue to be performative for the time being which is also unfortunate.
i was so burnt out upon entering MIT, and now i regret not taking a gap year or something. i feel like i missed out on a great learning opportunity
thank you for writing this. you opened a bit of a window into my past i haven't really processed
Not that great, necessarily. Sometimes I wish that I could simply be happy with a "normal" job that pays the bills. Instead of feeling like I have to pursue an academic career, just to be able to work on the problems I am interested in.
The people who win the math contests (And yes, who get into elite schools because of it) enjoy practice. That's the secret. Tao says the same thing about research mathematicians.
The people who hate it don't do well and it doesn't help their college applications.
He mentions that he was the only one on high school team who discovered how to triangulate a polygon, which is taught in Geometry class (junior high school for him).
Their bad attitude drags the team down.
This passage sticks out to me:
>I kept getting put into advanced mathematics classes while missing core concepts from previous years.... Eventually I was in classes with no standard curriculum at all, classes that had names like Discrete Mathematics and Advanced Topics II. To this day I have no idea what level of math they were meant to correspond to.
I don't know how an adult who has spent so much time actually trying to learn mathematics can maintain the hallucination that math is organized into "levels". The lack of a standard curriculum is an actual fucking blessing. God forbid someone except for the bureaucrats at pearson/macmillan and whatever federal committee decides on the standard curriculum for K-12 get to plan a math course. The author's opinion on this is backwards.
Moreover, he wasn't "lacking the core concepts" needed to take on these elementary topics, because there aren't any. That's the point. Math is built from nothing.
Second, you can feel the resentment in the author's voice when he talks about his friend who became a mathematician of sorts. And that resentment is that his friend is actually interested in mathematics. This is an interesting insight, but it's unrelated to his thesis.
We can gain more insight into the author's world view by considering some of his other essays. In "Math Team", he lists an impressive set of extra curriculars, but for some reason shies away from the mention of his church. However in [1] we see the following:
>Church was a big time commitment for us. We had prayer meetings on Tuesday night, Friday night youth group, Sunday services and Sunday school, and then Bible study later at night.
This is an altogether different account of how his time was spent as a youth. Maybe it's important to the author not to place anything online which would cause conflict with his parents, but it seems to me that the obvious thing putting too much pressure on his childhood time is this.
This essay on church is generally full of contradictions as well, for instance:
> [Church] makes it hard to be honest. In church we valued having deep, personal conversations with each other, but it felt like people always held something back.
followed not two paragraphs later by the exact opposite claim:
> It’s easier to trust a group of people if you know that you are all committed to the same things.
In [2], the author concludes with a summary of what he believes faith to be:
>Faith is not a process for choosing what to believe in or what to commit to. It is a tool for helping with what comes next. Creeping doubt and regression to status quo is natural, even in the absence of any new evidence. Faith is the virtue of counteracting that regression, through repeated internalization of those truths and commitments.
The conclusion I draw from this collection of essays, is that the author knows exactly what was wrong, but considers it a virtue to lie to themselves about it. Perhaps denying your natural doubts can sometimes be good for you, but to me it sounds a lot more like the spike protein on the mind virus of Christianity wreaking havoc. Regardless, if you're not willing to engage with your doubts, then you have no business putting your thoughts into an essay under the pretense of intellectual honesty.
1: https://www.benedict.one/2020/12/09/church-and-community/ 2: https://www.benedict.one/2020/03/02/faith/
I don't think much good comes from analyzing a private stranger in this way, especially given such limited evidence.
He is publicly making an argument that math team is dull and bad. The argument is based in the evidence of his personal experience, and the philosophy with which he approached this math team is very important context that he has left out, which undermines his claim.
He's also not a private stranger. He has 1500 followers on twitter, and an extensive blog about his personal life.
> if you're not willing to engage with your doubts, then you have no business putting your thoughts into an essay under the pretense of intellectual honesty.
kind of talking about every essay, ever? The only people free from doubt are on ventilators and definitely aren't writing a lot of essays. The very act of writing an essay is engaging with (a few of) your doubts. And if you're writing it for others to read, you're painting it over with some level of pretense.
Just because he's not engaging with your personal hobby horse of uncritically accepted Christianity doesn't mean he doesn't have something to say. Show me a being with a pure mind, free of any self-contradiction or self-avoidance.
Really, please do, so I can pet it and make it wag its tail.
> the author knows exactly what was wrong, but considers it a virtue to lie to themselves about it.
As do we all. Only the topic varies.
Absolutely not. Only the bad ones. An essay is an argument with yourself. If you take the explicit position that you should ignore your doubts, as this author does, then what you are putting on paper is your personal confirmation bias.
My hobby horse is not christianity, my hobby horse is the thing that he has insanely distilled from christianity as the part worth keeping. The author had a bad experience as a teen applying to elite colleges for no other reason than because he was supposed to, and the conclusion he should be drawing from this observation is so obvious that you might not even notice that he doesn't.
X = 0.acdabcdabcd... Y = 10000 * 0.abcdabcdabcd... = abcd.abcdabcdabcd...
Y - X = abcd.abcdabcd... - 0.abcdabcdabcd.. = abcd (without the pesky decimals)
I too learned this in high school and was fascinated by it.
It is far, far harder to qualify for an elite high school math team or get into Stanford now.
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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.
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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.
The author went to Stanford so what he experienced is 1000x whatever you are talking about