Splitting Rent with Triangles

You can find out how to fairly divide rent between three different people even when you don’t know the third person’s preferences! Find out how with Sperner’s Lemma.

Network Mathematics and Rival Factions

The theory of social networks allows us to mathematically model and analyze the relationships between governments, organizations and even the rival factions warring on Game of Thrones.

How to Generate Pseudorandom Numbers

What is a the difference between a random and a pseudorandom number? And what can pseudo random numbers allow us to do that random numbers can’t?

Kill the Mathematical Hydra

How do you defeat a creature that grows two heads for every one head you chop off? You do the math. Mathematician Kelsey Houston-Edwards explains how to defeat a seemingly undefeatable monster using a rather unexpected mathematical proof. In this episode you’ll see mathematician vs monster, thought vs ferocity, cardinal vs ordinal. You won’t want to miss it.

Are Prime Numbers Made Up?

Is math real or simply something made up by mathematicians? You can’t physically touch a number yet using numbers we’re able to build skyscrapers and launch rockets into space.

Stochastic Supertasks

Supertasks allow you to accomplish an infinite number of tasks in a finite amount of time. Find out how these paradoxical feats get even stranger once randomness is introduced. What happens when you try to empty an urn full of infinite balls? It turns out that whether the vase is empty or full at the end of an infinite amount of time depends on what order you try to empty it in.

Making Probability Mathematical

Throughout much of human history, people consciously and intentionally produced randomness. They frequently used dice – or dice-shaped animal bones and other random objects – to gamble, for entertainment, predict the future and communicate with deities. Despite all this engagement with controlled random processes, people didn’t really think of probability in mathematical terms prior to 1600.

Simplicial Complexes: Part 2

Last episode we saw that your neural network can be modeled as a graph, which — we’ll show in this episode — can be viewed as a higher-dimensional simplicial complex. So… what is a simplicial complex??

Your Mind Is Eight-Dimensional: Part 3

Last episode, we learned that your brain can be modeled as a simplicial complex. And algebraic topology can tell us the Betti numbers of that simplicial complex. Why is that helpful? Let’s find out.

What is a Random Walk?

Random Walks are used in finance, computer science, psychology, biology and dozens of other scientific fields. They’re one of the most frequently used mathematical processes. So exactly what are Random Walks and how do they work?

Crisis in the Foundation of Mathematics

What if the foundation that all of mathematics is built upon isn’t as firm as we thought it was?

Note: The natural numbers sometimes include zero and sometimes don’t — it depends on how you define it. Within logic, zero is always included as a natural number.

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