Yesterday I watched “King of Kong,” and a while ago I fell in love with “Spellbound.” Both of those movies are documentaries about strange subcultures of people — where the norms and values of these subjects are so foreign to the viewer that it’s a bit of an anthropological expedition.

While watching “King of Kong” I decided that a movie needs to be made about a mathcamp somewhere.

Some backstory: I went to mathcamp. Twice. And I was a counselor there once.

Those summers (especially those during high school) were transformative. I was one of those kids who were freakishly [1] good at math, astounded by the elegant beauty of it all, and I just got it. And I was always hunting for more. I would pick up second hand math books and study them, did the AMC (then AHSME) competitions, and did the write-in USAMTS competition. I was on my first high school’s math team (my second high school didn’t have one). And still, that wasn’t enough. I wanted to go to a place to study math for 5 weeks.

Seriously.

Mathcamp was the first time I had really been put in a place where I could geek out with my freak out. From 8am to 5pm (and then after dinner, well into the night), I would attend classes, work on problem sets, and enter group math challenges.I ate up — like a kid starved for sustenance — all the lectures. I was introduced to a ton of new mathematical topics (e.g. number theory, combinatorics, graph theory, abstract algebra, topology, linear algebra). I was finally challenged with problems which forced me to hit dead ends, do research, employ computer programs, and ask for help. To this day I bring my 2″ binder and 2 chalk-filled folders of mathcamp notes and handouts every place I move (Boston, LA, and now NYC). Looking through that binder, I found a copy of a letter I sent to a high school friend. Some excerpts:

Remember you said that most of the people here would have pocket protectors? It would seem that no one does. Or if they do, they left them at home. Actually, the people here are quite… hip. At least most of them… Another thing I noticed is that I’m really, really stupid. I see all these geniuses (genii) about me and I come to this epiphany. I realized that the true people I need to compete against when apply for college are these freaks of nature. They are naturally smart and they can learn any topic in a week (some even less); if I told someone to learn Einstein’s theory of relativity (general — not special), they would learn it, and by the looks of it, improve upon it, write a thesis, and submit it for peer review.

[…]

I need to convey to you all the hard stuff we get, [so] I will include a problem we got: Find all rational points on the graph of x^2+xy+y^2=2. I haven’t attempted this problem yet, though I think I know a way to solve it. Okay, that is fun.

Many of those who attended camp with me were in the lowest caste of their school’s totem pole. They dressed strangely, were interested in totally geeky things (e.g. role playing games, Rubik’s cubes, Douglas Hofstadter, linguistics, proving a theorem), and didn’t have a lot of people their age in their towns to connect with. Just as many others were “normal.” And yet (a few) others were clearly in their hometown’s popular crowd.

(If you’re curious, I wasn’t either an outcast or popular; I was involved in a bunch of activities, had a diverse group of friends, and really enjoyed my classes.)

What I learned from attending mathcamp was more than math. It showed me there were others like me, who were freaks of nature also. Who else could I talk to about spending 5 hours on a math problem and conquering it? Not my teacher, not my parents, not my sister. They would listen, kind souls, but they wouldn’t (couldn’t) understand the pain, the agony, and the swelling feeling of success. No one, but my eclectic, wonderful, creative colleagues, the mathcampers.

I helped create a yearbook both years I was there. The first yearbook was titled “We made room in the margin” (a not-so-subtle allusion to Fermat’s Last Theorem). The opening page read:

Here at Mathcamp, we strive to live in the image of Fermat and other mathematicians of his ilk, keeping alive the spark of discovery and the flame of passion, stirring the wonder and awe of beauty and truth that have compelled mathematicians prior to Fermat, and ever since, to make great leaps in human genius. However, we depart from dear Fermat in one way: we leave nothing about what went on here to be lost to eternity. Within these covers lie the work of a summer and the memories of a lifetime.

Some of the sayings on the yearbook pages seem to sum up what this was all about:

You might think you’re crazy (i.e. belong at Mathcamp) if you’ve ever: written numbers using an irrational base; written numbers using an imaginary base; computed the first 1,000,000 digits of the square root of 2; computed the first 1,000,000 digits of the square root of 4 (with amazing accuracy!); spent more on your calculator than on everything else combined; calculated transcendental functions by hand — for fun; memorized 1,000 digits of pi and forgotten your own telephone number.

and

I learnt a lot at Mathcamp, a lot about how beautiful and varied math is, “But as for everything else, so for a mathematical theory, beauty can be perceived by not explained.”–not in a few lines. I’ll write about something else I learnt, then, about myself. I learnt not to be afraid to try new things, to get the most from every moment. Also I want to be a part of something that lasts beyond the ‘limit’ of life. One of the best things at camp was meeting the coolest people–teachers and friends in one. I don’t suppose I can thank all of you enough for making this probably the best summer I’ve ever had.

It was summer camp. And in summer camp, the hierarchies that exist in high school vanish. And it was a time to celebrate that, let new bonds form, and let the thing that united us be our passion.

One of the reasons I wanted to be a math teacher from the earliest age is so that I could convey the same deep things I feel about mathematics to my students. It’s hard work, and I fail at it almost every day, but when a student exclaims without thinking “aaaah, I get it,” or “that’s really cool,” then I know I’m doing something right.

[Recollections inspired by a recent WildAboutMath blog posting]

[1] To be clear, I thought I was freakishly good in my small town. Until I went to mathcamp and realized that I was just squarely in the middle of the road there.