The math behind your daily annoyances
The most frustrating elevator rides aren't just bad luck—they're mathematically inevitable. When you're on a high floor and only one elevator serves your building, it's far more likely to arrive going the wrong way because the elevator spends more time traveling upward than downward at your floor. This counterintuitive phenomenon was first studied by physicists George Gamow and Marvin Stern in the 1950s, who found that the elevator goes the wrong direction five out of six times. The same kind of elegant math applies to sharing food: mathematicians have proven that no matter how unevenly toppings are distributed on a pizza, there’s always a way to cut it fairly so both people get equal dough and topping. Even more surprisingly, the same principle extends to three dimensions—there’s always a perfect cut for a ham sandwich that divides bread, ham, and bread equally. And when you shuffle a deck of 52 cards, you’re almost certainly creating a unique arrangement that no human has ever seen before—thanks to 52 factorial, a 68-digit number. These examples reveal that math isn’t just abstract theory; it’s woven into the fabric of daily life, from waiting for elevators to sharing a slice of pizza. The real takeaway? Math isn’t reserved for geniuses. Even the greatest mathematicians make simple mistakes—like confusing 57 for a prime number—proving that math is about curiosity and insight, not perfection.
When you're on a high floor with one elevator, it's five times more likely to arrive going the wrong way due to the physics of elevator travel patterns.
There's always a way to cut a pizza fairly so both people get equal dough and topping, even if the toppings are unevenly distributed.
A single shuffle of a 52-card deck creates a unique arrangement that has likely never existed before—thanks to 52 factorial, a 68-digit number.
The ham sandwich theorem proves there’s always a single plane that can cut a sandwich into two equal halves of bread, ham, and bread.
Even world-class mathematicians make basic mistakes—like Alexander Grothendieck mistaking 57 for a prime number—showing math is about ideas, not flawless calculation.
…and 3 more takeaways available in PodZeus
Introduction to Proof Positive
Rachel Feltman introduces the podcast and the guest, Menon Bischoff, and previews the theme of math in everyday life.
Why Elevators Always Go the Wrong Way
“The building is really plotting against you. And this is for mathematical reasons.”
The Pizza Theorem and Fair Sharing
“There's always some moment while you rotate your knife at which there's the same amount of the topping on both sides.”
From Pizza to Ham Sandwich: The 3D Version
“You will always find one cut that is perfect and that will just divide the sandwich fairly.”
Shuffling Cards and Writing History
“It's almost sure that you created a card arrangement that no human on the earth has ever created before.”
“even a genius like Rotendieck can be wrong on such simple stuff that shows that math is a lot about ideas and not just about calculating things.”
“Then it's almost sure that you created a card arrangement that no human on the earth has ever created before.”
“The building is really plotting against you. And this is for mathematical reasons.”
Host
Guest
Menon Bischoff
person
Rachel Feltman
person
Scientific American
organization
Proof Positive
other
George Gamow
person
Marvin Stern
person
Alexander Grothendieck
person
Spectrum
other
What’s in a name? When it comes to PCOS, a lot
15m • 6/5/2026
Disclosure Day and the science of alien language
15m • 6/12/2026
From the Vault: You’ve Got Pee-Mail, Part 3
51m • 5/30/2026
Karmelo Anthony Defense Implodes, Massive Philippines Earthquake, GLP-1 Cancer Study: AM Update 6/9
20m • 6/9/2026
From aspiring actress to NASA astrophysicist
22m • 6/15/2026
Start discovering podcast insights today
Start with a 7-day trial and explore a growing catalog of popular podcasts. No credit card required.
No credit card required • 7-day trial • Cancel anytime

