Elevators, pizza, and card shuffles: math at hand

math in – A theoretical physicist describes how everyday math can feel personal: why an elevator often arrives going the wrong way, how rotating a knife can make pizza-sharing fair, and why shuffling 52 cards can create a 68-digit arrangement no person has ever made bef

The elevator doesn’t just fail—it seems to turn itself into an accomplice.

In one building. the problem is intimate and immediate: press the button. wait for the arrival. and the first elevator that comes “just goes the wrong direction.” The delay feels like it’s aimed at you. And when the moment keeps repeating. it’s easy to call it Murphy’s law—bad luck with a good sense of timing.

But theoretical physicist and editor Manon Bischoff. speaking on Scientific American’s Science Quickly. says there’s a mathematical reason the building can feel like it’s plotting against you. The phenomenon was studied in the 1950s by physicists George Gamow and Marvin Stern. who were working in the same building on different floors and had only one elevator. They observed that the elevator that arrived first tended to go in the opposite direction. with Gamow tracking the pattern: five times out of six cases. the first elevator went the opposite direction.

The logic is surprisingly plain once it’s laid out. If you’re near the top of a building. most of the time an elevator reaching your floor must come from below and then. shortly afterward. be going down again. That means at your floor there’s only a tiny sliver of time when the elevator is actually traveling downward. The stretch of time when it’s traveling upward is much longer. If you arrive at a random moment. you’re much more likely to catch it while it’s going up rather than when it’s going down.

Bischoff didn’t discover the study through a formal assignment so much as through the way good ideas travel. “I was just doing some research. ” she said. and then read the small report Gamow and Stern produced—complete with jokes about the problem. She wrote it down, drew a simple diagram, and the “plotting against you” feeling snapped into something solvable.

The same kind of surprise shows up in how mathematicians think about splitting food. When Rachel Feltman asked about the newsletter’s idea that math can help us “live more deliciously,” Bischoff talked about optimally cutting a pizza.

The goal, she said, isn’t only that two people get equal amounts of dough; it’s that they also get equal amounts of topping. She described the everyday mismatch people often end up with—toppings crumbled in one place, the rest left bare—and then walked through the mathematical challenge of fairness.

A natural approach, Bischoff said, is to slice through the middle point of the pizza. But mathematically. if you don’t cut directly and instead rotate your knife slightly. the topping distribution changes smoothly from one half to the other rather than snapping abruptly. In that continuous shift. there has to be some moment during the rotation when the topping amount on both sides becomes equal.

The math doesn’t hand over a magic angle. “The mathematicians just proved that there is a solution,” Bischoff said, “but they didn’t tell you how you get it.” The search is part of the proof’s bargain: rotate, keep going, and eventually you hit the fair cut.

That idea of dividing more than one thing at once carries into a three-dimensional version too. Bischoff said mathematicians generalized the pizza result—treated as a two-dimensional disc with two objects. pizza dough and topping—to a ham sandwich. In that setup, there are three objects: one slice of bread, a slice of ham, and another slice of bread. The sandwich might not be carefully layered; the ham is “a little bit spread out.”.

Fairness. then. means finding a cut that divides everything in half: the upper part of the bread. the ham. and the lower part of the bread. Mathematicians showed that if you continuously vary the angles of that cut. smoothly. there will always be a perfect one that divides the sandwich fairly—again. in a way that depends on the continuity of the change.

Then Bischoff moved from cutting to shuffling—because math, she said, doesn’t just live in diagrams or food. It lives in the everyday act of mixing.

Every time someone shuffles a deck of cards. she said. it’s possible to create an arrangement that no human on Earth has ever created before. The reason is numerical, almost absurdly large. With 52 cards, the number of possible arrangements is 52 factorial, written as 52!, which equals 52 × 51 × 50 × 49 down to 2 × 1. Bischoff called it a “68-digit number. ” a scale so vast that once one particular arrangement exists. the chance of another person landing on the exact same arrangement becomes “so low” that it’s plausible to think it’s effectively the first time.

Her point wasn’t about proving certainty; it was about showing how quickly the ordinary becomes staggering when the math is taken seriously.

By the end of the conversation, Feltman asked what Bischoff wished people knew about math—and what misunderstanding keeps it out of reach for people who assume it’s not for them.

Bischoff said one big myth is that you need to be “very intelligent or… a genius” to understand math or to like math. That belief, she argued, is wrong. Interest is enough to start, because math contains many stories and facts that can fascinate almost anyone.

She also challenged the idea that mathematicians never make mistakes. A favorite example was Alexander Grothendieck, one of the most influential mathematicians of the 20th century. In an anecdote, a colleague asked him for “a prime number.” Grothendieck answered 57. It sounds prime, Bischoff noted—but it isn’t, because 57 is divisible by 3. It’s a simple check. she said. and that’s exactly the lesson: even a mind celebrated for complex work can be wrong on something straightforward. For her, the episode shows math is about ideas, not just calculating speed.

And maybe that’s what makes the elevator story land. It’s not that math makes life fair or convenient every time. It’s that when the world feels like it’s singling you out—pressing the button. rotating the knife. shuffling the deck—there’s usually a reason behind the drama. Sometimes the reason is sitting quietly in the numbers all along, waiting for someone to draw the diagram.

math in everyday life elevator paradox Gamow Stern pizza cutting theorem ham sandwich theorem card shuffling arrangements Grothendieck 57 Scientific American Proof Positive Science Quickly