What We Say When We Speak of Puzzles: Part I

In high school, I remember sitting on my bed in our four-person dorm room, lifting my head from a notebook filled with math problems and realizing that it had been six hours since I had last looked up. It was a four-hundred-page notebook, the biggest and most expensive we could buy in our small boarding school shop. My handwriting in it was cramped, clear only to me. I wrote no topic or subject headings or page numbers, and yet I knew exactly where in the book I had solved particular problems—this book was an extension of my mind.

It was dark outside the window now, where the last time I looked it had been bright. I felt a distinct combination of both pride and fear, not understanding how I could lose myself in this way but also believing that it was this capacity to focus that made me exceptional. I took this kind of falling into focus to mean that I loved mathematics. The mathematical world had long been both more challenging and less complicated than the human world I was escaping from. It was ordered and soluble, and all I had to do was understand the logic, solve the problem. And I was good at that. In math, I could predict what would happen if I did everything right.

About a decade earlier, I had to prepare for the entrance exam that would get me into boarding school. And so my usual after-school routine of sitting quietly, out of sight and mind in the office of my parents’ architectural design firm, was now punctuated with running up to my father’s desk to receive from him a new instalment of math problems, written out in one of his notepads. Even just the medium thrilled me—these were notepads reserved for serious stuff! I’d rush off to solve the sums, quietly in another room, and then rush back to show him my work. I remember feeling proud of myself, not just for getting the math right but for figuring out a safe way to be visible in this grown-up space where I, a child, spent so much of my day.  

At around that time, the people that worked for my parents talked to me. They took me with them when they went on little excursions to the printers, maybe get me a treat when they went to the shops, as though I were a little, loved dog. Looking back, I’d guess that they felt a little bit sorry for this quiet girl who skulked around their adult workplace, who never played. If so, they did me the kindness of hiding their pity. 

On my birthday, they brought me presents, and I remember feeling special.

A few days later, my mother was angry at these people who were kind to me. Such anger wasn’t unusual. They were being blamed for an error that may or may not have been their fault, and as we drove back home late that night, my mother was not yet calm. And so, as usual, she talked and talked through her anger as my father silently listened, interjecting noncommittal affirmations with a well-practiced cadence. In the backseat of the car, as usual, I listened while pretending to myself that I wasn’t there. My mother went on and on, trying to divine a reason for the error—why had her staff been so incompetent? Part of her list of reasons, of course, was that they’d been distracted from their jobs by my birthday. And so it was simple. From that moment onwards, I loved mathematics and hated my birthday.

Mathematics functioned in my life as a kind of armor. As long as I was doing well in math class, I was, by some objective measure, okay. I conjectured that being okay was enough for my parents to leave me alone because, in our world, it felt like the opposite of alone was ire. Math was both a country in which I could be alone and the passport that let me stay there.

So it felt like a crisis when the principal at my boarding school, himself a mathematician, wrote with some concern on my tenth-grade report card about my “unaccountable diffidence.” If I was so very good at doing the work that my math class expected of me, why didn’t I push myself to go further, beyond the text book? Could I, perhaps, set my sights on becoming a mathematician? My mother asked me over and over about my unaccountable diffidence, and in her insistence I knew, with a sinking feeling, that I’d have to do more, if only to assuage her worry. My path towards a life of the mind began here, in resignation.

I asked the principal for more math, advanced math that would prove I was the opposite of diffident, and he was only too happy to give me his own copy of A First Course in Abstract Algebra by John B. Fraleigh. I wonder now how much thought he put into that choice. Why abstract algebra, why Fraleigh?  Whatever his reasons, he made a good choice. To this day, pulling his-and-then-my copy of Fraleigh off my bookshelf feels like a bracing pat on the back from a kindly uncle. Through the thin paper of its pages, I can see the text that has passed and the text that is yet to come casting shadows on the text I am reading, and so I know I’m on a journey, a quest even. Fraleigh’s voice on the page is friendly, welcoming, making me feel like math is somewhere I am meant to be. He writes:

Suppose that you are a visitor to a strange civilization in a strange world and you are observing one of the creatures of this world drilling a class of fellow creatures in the addition of numbers. Suppose also that you have not been told that the class is learning to add, but that you were just placed as an observer in the room where this was going on. You are asked to give a report on exactly what happens. The teacher makes noises that sound to you approximately like gloop, poyt. The class responds with bimt. The teacher then gives ompt, gaft, and the class responds with poyt. What are they doing? You cannot report that they are adding numbers, for you do not even know that the sounds are representing numbers. Of course, you do realize that there is communication going on. All you can say with certainty is that these creatures know some rule, so that when certain pairs of things are designated in their language, one after another, like gloop, poyt, they are able to agree on a response, bimt.

Which is to say, I learnt from Fraleigh that algebra is actually about communication. Algebra made the reality of communication—messy at the best of times, and in my family, usually fraught—into a safe abstraction, where rules could be followed and outcomes predicted by logic. By burying myself in algebra, I could prove I wasn’t diffident, thus avoiding adult scrutiny. But by taking algebra seriously, I could use my logical skills—skills forged in trying to make sense of my parents’ silence, fear, and anger—to grasp at what it means to communicate.

There is a tension that can animate a life of the mind, the tension between abstraction and material reality. And in my life, this tension grew intertwined with another tension, between fear of the world and a deep need to communicate with it. In school, what pulled me out of my heady terrifying mathematical reveries was often the sound of the dining hall bell, indicating that it was time to eat. At dinner in school, I had to sit in the real world, outside of my head, with people that didn’t care very much about abstract algebra. Conversely, Fraleigh didn’t seem like he cared much about the agonizingly silly thing I may have said at dinner. Straddling two worlds, each could provide temporary refuge from the hardships of the other.

But at home, I lived in fear of the question What are you doing? and abstract algebra wasn’t a good enough answer. What are you doing? was the question that replaced all others. My answer was expected to hold, and yet somehow also mask, my feelings, hopes, and struggles. The consequences wouldn’t be good if my answer to that question triggered my mother’s anxiety, or ire, or judgement, all of which could stem from her incomprehension. My mother was brilliant, and so she expected to understand what I was up to. It was through her understanding of my intellectual endeavors that we connected, and abstract algebra risked severing this connection even as it allayed fears that I was diffident.

These tensions—between fear and connection, abstraction and the material—poured themselves into a puzzle that became a central captivation of my teenage mind: The Soma Cube. A puzzle designed by a Danish polymath-of-sorts, Piet Hein, the Soma Cube is a cube that is broken into seven pieces, each of which is a configuration of three or four cubes whose sides are one third the length of the original cube. Each of the seven pieces is ‘irregular,’ which in this rather specific context means that you can draw a line connecting two vertices of the piece such that this line lies entirely outside of the piece. These seven pieces are the only irregular configurations that can be made up of three or four cubes, and, remarkably, these seven pieces fit together in two hundred and forty unique arrangements to make up the larger cube we started with.

There is a constricted sense of beauty to the Soma Cube, to the notion that all possible irregularity fits together to create something regular. Two of these cubes lived in my childhood home, and on idle afternoons, my parents occasionally took them apart and solved them by a sort of trial and error. My father had one favored solution, my mother another, and neither had the necessary combination of patience and motivation required to search for any of the remaining two hundred and thirty-eight. But armed with a growing dexterity in wielding abstraction from my forays into algebra, I realized I could do more. Not only could I find other solutions to the Soma Cube, I could use mathematics to search for a way to find all the solutions. This was a safe answer to What are you doing?

The exercise of solving the Soma Cube systematically transmuted all of my other animating tensions into a single, singular one—between possibility and constraint. A cube has eight corners and six faces, always and eternally. Each piece had the potential to occupy only certain combinations of corners and face centers, and there are only so many ways in which these combinations can add to eight and six. But beyond these constraints, there is possibility, the kind that allows for long, lonely afternoons spent with my hands busy, positioning and repositioning pieces until they fit together just so.

And yet I understood that this puzzle solving was not true discovery. I knew that I was not the first to solve this puzzle entirely, and with dial-up internet at my disposal in my parents’ office, I could even look the solutions up. But to do so would have been to relinquish my armor, and so I didn’t.

But again, that tension between fear and reaching out. I never looked up all the solutions, but I did search the internet for information on the Soma Cube, learning as much about it as I could without cheating on my quest to solve it completely. I found the website of someone named Thorleif Bundgaard. Bundgaard seemed as captivated by this puzzle as I was. And through his website—blocky and unsophisticated to this day—I learnt more about Piet Hein, the mind that made the puzzle that served, years later and miles away, as a frightened teenager’s shield.

Reading the first email I sent to Thorleif, it seems that I was looking for nothing more than reassurance that my endeavor was worthwhile, this fundamental question—am I enough?—couched in the language of simple curiosities about the puzzle itself. His answer—immediate, clear, and kind—did reassure me. He signed his email “Friendliest Thorleif,” and maybe that’s why I found it in me to ask, “just as a matter of interest, which country are you from?”. The exchange that followed was true human communication—delightful, tentative, and a bit confused. I liked hearing about Denmark, I was peeved when Thorleif corrected my misconceptions about Piet Hein, and I was grateful when he explained, syllable by syllable, how to pronounce his name and Hein’s correctly. I shared information with him—about my school, my upcoming exams—that he did not ask for. And most lastingly, Thorleif introduced me to another of Piet Hein’s creations, short aphoristic poems called ‘grooks.’  Here’s one:

The Road to Wisdom

The road to wisdom? Well, it’s plain

And simple to express:


and err

and err again,

but less

and less

and less.

I spent weeks, months, with the Soma Cube, in a space of trial and error. I hadn’t paid much mind—thank goodness—to the foreword to my Indian edition of A First Course in Abstract Algebra, where D.N. Verma wrote that seeking to solve such mathematical puzzles was but an infantile fascination. But in time, I abandoned the Soma Cube and my search for all its solutions. With a little distance I could see quite clearly that my fascination with Soma Cube had been infantile. But the thing about infants is that they know somehow, inexplicably and unconsciously, exactly what they need and, often against all odds, they ask and ask and ask until their needs are met. I held onto the Soma Cube until it delivered me deeper human connection, and then I moved on.

(This is Part I of the memoir writing I’ve been working on. There will be a Part II and a Part III, that will make their way into the world in various shapes and forms in the near-ish future. Keep an eye out for them; I’ll be linking to them here for sure, and thank you for reading.)