PROMYS Year 3

I got back from another summer at PROMYS last week. A really quick summary of my experience was that it was a lot of fun, maybe even too much.

Let me explain:
I had a ton of fun this year hanging out with friends and meeting new people, but the math was honestly underwhelming. This year the advanced seminars were on Modular Forms, Primes and Zeta Functions, and Algebra. I didn't do Algebra, since I figured I already knew a lot of the material (it also happened to be low-quality, in the sense of the PROMYS tradition and difficulty, so I got lucky). I think Marjory Baruch (the lecturer) tends to give seminars on stuff that is less profound and treats her advanced seminar (at least this and last year's) more like a typical college class: the PSETs just help you remember the class' content. That's the perspective of an outsider looking in though.

I thought Modular Forms would be very, very challenging since the topic of modular forms is an idea that runs extremely deep in number theory: it was used in Wiles' proof of Fermat's Last Theorem, there was a conjecture called the "Monstrous Moonshine Conjecture" for how outlandish it was to connect modular forms to something (it is proven), and in general just connects a huge amount of number theory to other stuff. The description of the class made it seem quite challenging, with lots of stuff that will have to be "taken on faith". I was really excited for this class. But it turned out to be a bit of a letdown. The lectures were a bit slow for my taste and the PSETs weren't very fun. There was just a lot of verification and insight-killing questions. Also, his lecture style was to present a proof of something major, and along the way assume certain lemmas. Then he would either leave the lemmas for the PSETs or prove them later in the summer. This just sucked the joy out of finding your own solution and insights. I feel like there was very little discovery here. The lecturer was a really cool guy though. It probably would've been best if he left making the PSETs to someone else. The Primes class was, IMO, a spiritual successor for first-year number theory. The PSETs were pretty high-quality in getting you to try and discover the mathematics going on (lecture was also terribly behind, but by design). Tragically, truly tragically, I wasn't that interested in L-functions. I just didn't find them that exciting. Even the first, "toy" problem that's supposed to hook you into the zeta function just wasn't that interesting to me. We did learn a really cool proof of quadratic reciprocity though.

The biggest mathematical redeemer was definitely the people. I had awesome conversations with really smart people this year. Last year I mostly just hung out with my returning friends, so I didn't interact with many first-years or counselors. But damn they're smart. This year there wasn't a whole lot of algebraic stuff in the seminars, but there was quite a lot more guest lectures about algebraic stuff. There was also mathematically adjacent stuff that I got to experience this year, like giving more presentations and even giving a minicourse! Man I suck at giving talks. It's good that I got to practice.

The people, as usual, were very cool and fun. I made an active effort (mostly near the beginning) to try and get to know more first-years, to compensate for last year. I think this plus me being a third-year plus my joy in messing with people's inventories (the definitions people made for what the integers are) led some people to think I was a junior counselor when I was really an imposter. So I became an "honorary JC". I got to occasionally wake people up for lecture, go to counselor seminars,, give a minicourse (only counselors and JCs are supposed to give these), helped in some review talks, and got the JC role in Discord (which probably confused people more 😭). I was particularly impressed with the emotional maturity and passion of a first-year. Overall, I feel like the first-year culture is quite a lot bolder this year: they organized a lot of extra events like karaoke and one of them even gave a minicourse (though it was in a weird spot between official and unofficial).

Overall this was another good summer, but throughout it felt like I've outgrown this camp a bit. There weren't any interesting algebraic seminars, none of my good friends from my first-year returned (except for one, who even has a blog! https://listed.to/@angelofd3sth), and seeing the friend groups form was just so bitter-wholesome. I still had a ton of fun; I just think that this is the right time for me to stop PROMYS, at least for a while. It just seems like a poetic point for closure: high school ending, friend groups separating (I also hung out with a group of second-years a decent amount), and my algebra knowledge being in a weird place between student and counselor.

I know someone who was a fourth year student last year, and I just can't imagine it. They're sort of the one that's "still standing after all this time" of all their friend groups. I can't imagine being a counselor is a whole lot better mathematically: I went to a decent number of the counselor seminars, and they aren't close to the experience of an advanced seminar (they lack cohesion, psets, tend to be quite specialized, and they're just not made for that). I'd probably see new and interesting ideas in grading people's PSETs and talking to them, but I don't think that'd be a similar experience to PROMYS.

Just some other fun memories:
Talent show: I video called one of our professors, did karaoke for Chainsawman's Kickback (the intro song), the building started leaking, tons of chaos as time ran out
park shenanigans: on the way back from seeing Hamlet we saw a park and started playing on it, but it was closed and eventually the police arrived (there were a lot a lot of people playing on it)
fish: there's a high skill card game we like to play called Fish, and typically I do alright and one of my friends does really good, but somehow whenever we're on the same team we do awful, like really awful, until the last night when we reverse swept a game; my friend group was 6 people, so enough for 2 fish teams in a fish tournament. there were 3 jcs and 3 not jcs, so we formed the JCs team and the real JCs team. we got swept. even one of our professors/program admins joined in the tournament
the math/stat/cs building is very modern in architecture, the view from the 17th floor is beautiful
mit museum: first time I had chocolate pizza, was pretty cool
boba: once we walked like 30 minutes to a different university to get boba because the places nearby were closed
hamlet: unexpectedly good, also was partly in Spanish
had Indian food for the first time
bananas: one of the professors hates bananas, and as a prank some students got hundred of bananas and put them on this comically small table before his lecture
gym: started going to the gym for the first time
frisbee: some people on our side got cuts; we also got destroyed in terms of points
american psycho: we got a bunch of asian snacks and sparking cidar and brought it into some classroom to watch the movie