Inside Math Circle: A Perspective by Adam Lange

Inside Math Circle: Perspective by Adam Lange

This piece is modified from an essay called Running with Wolves written by Adam Lange. Adam volunteered for SF Math Circle while taking a Mathematical Circles course at USF, taught by Dr. Paul Zeitz.

 “By concentrating on what, and leaving out why, mathematics is reduced to an empty shell.”

—Paul Lockhart

The sun slithers its lanky arms through the clouded window and slaps the back of my neck into a red, sweaty oblivion, but I, sitting at my desk, pencil in hand, ready to diligently scribble away at my notebook, take no note. It’s math class, and a little bit of solar abuse won’t stop my paying attention. As my teacher Cyrilly begins, speaking on the wonders of multiplication and explaining to us for the hundredth time how to multiply three-digit numbers, my nostrils are stung by the pungent smells of sweat and flatulence. Holy $!@#, I think to myself when I finish multiplying 321 by 202, this is so easy! Why do we have to go over this again? These imbeciles in my “upper level” math class can’t differentiate a plus sign from their own mothers, let alone multiply three-digit numbers! That combined with the unpleasant aroma wafting up from in front of me makes this day in math class a bit uninspired. I mean, really, people, three digits is just like two digits but with an extra number.

My mind slows, my pencil now meandering to form hearts and smiley faces all over my page. I begin to think about the contents of my lunchbox instead of what’s on the paper in front of me. My eyes take on a blank glaze, the daydreams flooding in, and just when I’m about to save my classmates from the mundane torture of multiplication by flying them off on my dragon, sword in hand, and leaving Foundations School Community behind in a curtain of flame like some kind of anime-status hero, a tap on the shoulder.

                  “What are you drawing?” Cyrilly asks, in her calm and caring way.

                  Busted. “Nothing,” I say, my face instantly turning a shade to match the back of my neck. She looks down at me, not with the mean spirit of a cruel teacher but with the compassion of an old friend, and after a quick back-and-forth, she asks me why I’m doodling and not doing my work.

                  “Well, ‘cause I get it,” I say, doing a quick multiplication to prove my point.

                  Impressed with my fast math (I give myself a mental fist bump), she stands back and thinks. After a brief moment of silence, she points to my paper. “Well, why don’t you tell me why this works?” I look back at her, puzzled. She pulls up a chair. “Like,” she continues, seeing my confusion, “why can we just carry that one and then add it the next multiplication?”

                  After some careful deliberation which gets me absolutely nowhere, I say, matter-of-factly, “Well,” and spew something out, trying to sound all cool and learned. Cyrilly just stands up, pats me on the head, and says, “Think about it,” and then she just walks away. And let me tell you, I thought about it. INSERTED: Oh, man, did I think about it.


Walking into the first Math Circle of the semester at the June Jordan School for Equity, I was racked with nerves. Excited, yes, but more than a little worried. I mean, I’d never really done anything like this before. I’d been in charge of kids a lot, sure, like when I worked as a counselor at that summer camp and had to deal with twenty kids every day screaming about how hot it was or how they needed something from me right now, or when I had that babysitting job and somehow managed to survive a few one-on-one or one-on-who-knows-how-many-kids-they-have hours (and at ten bucks an hour, I made bank), but this was different. This was a classroom setting and I was a teacher’s assistant. Here were some kids who were about to be taught a quick lesson and then sent to the wolves to run free, thoughts running rampant, and here I was, jogging beside them, trying to keep them on track. Unfortunately I didn’t have a sword and a dragon this time around, just a pencil and paper.

I suppose I was being dramatic, but this was nerve-racking! Regardless, I tried to contain myself. In choir they tell you to think of your nerves as excitement, channel them to help you do a good job. Well, I thought to myself. You want to be a teacher right? Here goes! And with that, I took the plunge.

 Adam Lange on the left, with students in the Middle School class at Lowell High School. 

Adam Lange on the left, with students in the Middle School class at Lowell High School. 

It went much better than the neurotic Jewish mother in me was telling me it would. The kids asked interesting questions, and they seemed to be intrigued by the subject matter, for the most part. And over the three weeks I was there, the group grew a little bit, and the new kids seemed to enjoy it too. It was a similar situation at Lowell High School, the second Math Circle I was helping out with. The students seemed to really be enjoying what they were doing. Maybe it was the teachers who had interesting new concepts to share; maybe it was the freedom of the environment that helped these students feel at ease with the subject of math, which is often made scary rather than fun; maybe it was the extra credit some teachers were giving their students for attending; whatever the reason, the kids were invested. Yeah, sure, there were a couple who clearly didn’t want to be there, but overall, the air was teeming with genuine curiosity that prickled the skin, leaving hairs standing on edge for the anticipation of an unsolved question.


I’ve been sitting for hours in my room, taking different numbers and multiplying them together like a calculator out for a joyride. One-digit, two-digit, three-digit numbers. Still I feel no closer to an answer. I sit at my desk, looking blankly down at paper littered with ink-covered holes from overly-excited penmanship. I sit and I stare for who knows how long (minutes?, hours?), and I keep staring until I can’t stare anymore. Then I take my paper and angrily shove it in my bag. “Screw this,” I say aloud to an empty room, and I shuffle out the door and head to the living room, hoping to find solace in an episode of Teen Titans. I’ll ask Cyrilly about it tomorrow.


It is a very interesting experience, after having been subjected to years of what Paul Lockhart describes as “the confused heap of destructive disinformation known as ‘the mathematics curriculum,’ “ to come into a room so full of excitement that you can almost feel the pulse of energy over the crowd, a ubiquitous warmth fueled by sheer curiosity. That was exactly the case when I walked into the Marin Math Circle. I already thought the kids at June Jordan and Lowell were smart, but this was a room full of fifty little Einsteins, all at the edge of their seats! One of them, I was told, was already taking math classes at Berkeley in ninth grade! They were all so utterly in love with everything they were doing; I had never seen anything like it. They all reveled in the unseen oasis of mathematics, washed themselves in the cool waters pouring out from the whiteboard in front of them, practically climaxing at the very thought of discovering the secret truth offered up by the probability question their instructor was now writing on the board, chock-full of amazement and intrigue. There was little hesitation among them; if they had an idea, you can bet they were going to share it, and let me tell you, they all had ideas. You couldn’t ask a single question without half the class raising their hands in response. They were trampling over each other to get to the right answer first.

Meanwhile, I sat back, jaw gaping, lost. I could faintly hear the neurotic Jewish mother bubbling up inside me, saying in her full voice, straight out of the Bronx (Jewish mothers always have a Bronx accent, no matter their origin): Oh, that Adam, he’s not so great! You know this kid in ninth grade he was working with stumped him with a proof! She cackled shrilly in my head, went on about how much better my sisters were, and died out. Just like a Jew, isn’t it? Throw down an insult and then just let it slide by, make it fester in the ears of the object of your dissatisfaction, make them know what you think but then leave it up to them to process their emotions to whatever detrimental extreme that might be taken. Leave it to the Jews to make you feel like an unaccomplished piece of shit.

INSERTED: Wow, I think to myself, I wish I were this smart. I mean, seriously, I had no clue what was going on. This was beyond me. I felt defeated. I checked my phone: only thirty more minutes. Thank god! Something was clearly different here from the San Francisco Math Circle. A mere observer, I tried to work it out. I noted that there wasn’t much struggle. These kids didn’t require much guidance. Just like the kids at Lowell and June Jordan, they were given some of a concept and then thrown to the wolves. The difference here, however, was that these kids didn’t want or need a protector. They worked through their own thoughts, void of any sort of guidance from anyone in charge. Where at Lowell and June Jordan there were instructors and assistants, here there was only an instructor and a room full of kids (and a lot of parents who sat in the back of the room on their phones whose presence, quite frankly, seemed extremely unnecessary; way to helicopter your kids, guys).


I ask Cyrilly the next day at school to explain it to me. I tell her how much I’ve been working on it, how it’s kept me up at night, how I forgot to do my reading for English last night because I had been too focused on the math problem at hand — though the four episodes of Teen Titans I watched didn’t help read Roald Dahl’s poem either. But what does Cyrilly say to me?

“You’ll get it. Keep thinking it over!”

She pats me on the head, but all I feel is the condescending weight of five fingers pressing down on my reddish curls. I walk away, trying to throw on the best air of annoyance I can possibly muster. With no help from Cyrilly, a mother who is practically dyslexic when it comes to math, and a father who works until hours too late for my interest to still be peaked, I am left on my own to solve this seemingly-impossible problem.

It wouldn’t be until two weeks later that I start to understand it a little. Of course, at that point it would be just a little thought, a fragment of an idea, but over time, it would develop itself into a full-fledged comprehension. That would be one of those moments I would never forget, permanently burned into my brain as my first real self-guided, self-realized solution to an up-until-then incomparably difficult problem. Unaccompanied, I will have traveled great lengths, climbed imposing peaks, sailed choppy waters, all for the great joy of solving an intrinsically interesting math problem. (Wow, I’m a nerd.) Oh, the wonders that can be found through mathematics when simple concepts are coupled with a complete and total unwillingness to fail. To err, that’s a different story. That’s impossible to avoid. But even in the face of so many errors, countless dead-ends, constant landslides burying your thoughts in confusion, making you dig your way out of a seemingly-endless mound of $!#@ that piles on top of you more and more with every passing minute, it is this stubbornness for failure that pushed me, pushed the kids at Lowell and June Jordan and Marin, and has pushed centuries of mathematicians forward. Our swords might be pencils, our dragons mere sheets of blank paper, but the fire is real; it burns bright inside me and inside all the kids I worked with in Math Circle. And that miraculous flame will rage unhindered until my lungs garble out their last bit of air and my thoughts are left to fester in the minds of the next generations and so on and so on until there is nothing left to be worked out.