The math behind your daily annoyances

Science Quickly13mJune 3, 2026
AI-Generated Summary

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.

Key Takeaways
1

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.

2

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.

3

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.

4

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.

5

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

Chapters
0:13
1 min

Introduction to Proof Positive

Rachel Feltman introduces the podcast and the guest, Menon Bischoff, and previews the theme of math in everyday life.

1:01
1 min

Why Elevators Always Go the Wrong Way

The building is really plotting against you. And this is for mathematical reasons.

Highlight
2:58
1 min

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.

Highlight
5:53
1 min

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.

Highlight
7:31
1 min

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.

Highlight
High-Impact Quotes
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.
Menon Bischoff10:19
Then it's almost sure that you created a card arrangement that no human on the earth has ever created before.
Menon Bischoff8:04
The building is really plotting against you. And this is for mathematical reasons.
Menon Bischoff1:36
Speakers

Host

Rachel Feltman

Guest

Menon Bischoff
Topics Discussed
math in everyday life95%elevator math90%card shuffling probability88%52 factorial86%pizza theorem85%mathematical fairness82%ham sandwich theorem80%prime number misconception75%
People & Brands

Menon Bischoff

person

10xNeutral

Rachel Feltman

person

8xNeutral

Scientific American

organization

5xNeutral

Proof Positive

other

4xPositive

George Gamow

person

4xNeutral

Marvin Stern

person

3xNeutral

Alexander Grothendieck

person

3xNeutral

Spectrum

other

2xNeutral

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