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.

## Tag: PBS Infinite Series

## 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

## 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?

## What Does It Mean to Be a Number? (The Peano Axioms)

If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it?

## Unraveling DNA with Rational Tangles

When you think about math, what do you think of? Numbers? Equations? Patterns maybe? How about… knots? As in, actual tangles and knots?

## Crisis in the Foundation of Mathematics

## Can a Chess Piece Explain Markov Chains?

## Singularities Explained

## A Breakthrough in Higher Dimensional Spheres

Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent revelations in sphere packing have exposed truths about 8 and 24 dimensions that we don’t even understand in 4 dimensions.