In Third Grade, we all hated arithmetic until Mrs. Podolski, with her heavy Polish accent, showed up and briefly cast a numerical spell on us. Mrs. Podolski was a short, stout woman who replaced our regular teacher for two weeks. She wore brilliant floral print dresses and prefaced almost everything she said with, “And now, children.”
“And now, children,” she said during Arithmetic, “if you learn anything from me, you must learn never to divide by zero. It will explode and we will all die.”
If she was joking, nobody laughed. With Mrs. Close, our regular teacher, arithmetic had been silly counting games, adding up pocket change, dividing fruit and slices of pizza. It was rote memorization and multiplication tables—safe and boring.
For Mrs. Podolski, every number was special. One was sent to us directly by God and was unique; two, like our parents and eyes, was also divine. Three grew abundantly on trees in the savannahs of Africa and four was a cornerstone for geometry, pyramids and cathedrals. She had a special fondness for zero.
“And now, children,” she said, “I will tell you the secrets of nothing.” We held our breath.
She told us zero was like an enormous empty vessel—made of the finest china—waiting to be filled. But nothing could fill it, not apples and oranges, not our wishes or dreams. Nothing could even enter it, not even the tiniest grain of sand. Mysteriously, if you added zero to other numbers, it loomed invisibly in the background and nothing happened. But if you multiplied by zero, zero destroyed the number and turned it into nothing. The consequences of dividing by zero were even more severe: pure and utter destruction.
This was new. When Mrs. Close mentioned dividing by zero she only said never to do it, that it was against the rules. And we added it to the growing list of school don’ts: don’t be late, don’t chew gum, don’t talk without raising your hand, and don’t ever divide by zero. With Mrs. Podolski, we were fascinated and stupefied. Could numbers really have such power?
I didn’t believe it. On my homework, when ten was divided by five, I imagined five slipping inside ten and splitting it apart until only two was left. I thought of three going into nine with scissors and making three equal bits of nine. I put one into four so quietly that four didn’t even notice and stayed four. But zero was another matter. On the bottom of the page, I doodled about and played with dividing six by zero, seven by zero and eight by zero. They wouldn’t explode at all, I thought. They would each become like unicyclists and ride away, never to come back. They would disappear, not explode.
The next day, Mrs. Podolski called me to the front of the class. She held my homework up and I could see the red “F” on it. “And now, children,” she said, “we will see the consequences of dividing by zero.” I stood next to her nervously and she handed me a china tea pot. Perfectly smooth with a delicate pattern of a dragon wrapped around it, it was the most precious thing I ever held.
“And now, children, he will drop it.”
My jaw fell open as I looked at her. The whole class stared at me.
“Drop it, I say.” She furrowed her brows and nodded at the same time. I held the teapot tightly. It was cool to my touch.
“What are you waiting for? You want to put zero on the bottom. Let’s see what happens!”
If this was another of her jokes, I now despised her for it.
“Go on, drop it,” she said.
“I don’t want to,” I finally said.
“Here,” she said. She took the teapot from my hands and held it above her head. Then she let it go. Instinctively, I jumped back and when the teapot hit the ground, it exploded into millions of glittering pieces. Even the lid was destroyed. Some of the girls screamed, including Olivia Conn who always wore her hair in pigtails and never spoke. Michael Black, who sat in the second row and wore glasses, got hit in the leg with a piece of the handle and cried, “Ow!” My classmates in the front row got spattered with debris and when the shock wore off, a couple of them began to whimper. It was the math demo to end all math demos.
“And now, child, you may sit,” she said.
I looked at the shards on the floor, saw the commotion around me and wanted to be sick. As I walked back to my desk, I heard the crunching under my feet.
Mrs. Podolski dusted off her dress and bent over to pick up a handful of the destroyed teapot. Instead of putting it in the garbage can, she walked around the classroom and handed each of us a piece. As she went we could hear her say, “One for you and one for you.”
When she got to me, I reluctantly put out my hand and she said, “And one for you, child.” And she put nothing into my hand.
Just then, the Vice Principal, Mrs. Lamb poked her head in the door. “Is everything okay, I thought I felt an earthquake coming from this room.”
“No, everything is not okay,” Mrs. Podolski said, shaking her finger in the air, “one of your students just divided by zero.”
Mrs. Lamb gasped. “Didn’t you warn them?”
“Yes,” Mrs. Podolski said as she continued around the room, “but one was stubborn.”
“Shall we dangle him by his ankles above the black hole that just formed in the parking lot?”
“I don’t think that will be necessary,” Mrs. Podolski said, “I’m giving them nothing to think about. They can give some to their friends and their friends’ friends until everyone in the world many times over has some.”
Without raising our hands, several of us blurted out, “But you’ve given us nothing!”
“Yes, children,” she said, “if I divide the pot into zero pieces everyone gets nothing and if I divide it into pieces so small no one can see them, then everyone, and I do mean everyone, again gets nothing. But infinity is a topic for another day.
What she said hadn’t sunk in yet for all I could think was teapot + floor = big explosion or teapot / floor = shards upon shards. But the next day, Michael Black’s grandmother died, Olivia Conn couldn’t come to school because her parents’ basement flooded, and Russia got hit by another meteorite. I didn’t know if any of these were connected, but I never divided by zero ever again.
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Daniel Hudon is an unapologetic Canadian who spends his days educating a subset of the masses and his nights wondering why moonlight is so darn enchanting. He is the author of “The Bluffer’s Guide to the Cosmos” and “Brief Eulogies for Lost Animals: An Extinction Reader,” named a Must Read in the 2019 Mass Book Awards. He hangs out at danielhudon.com and @daniel_hudon.