There are lots of unsolved mysteries in the world of math, and many of them start off with a deceptively simple premise, like: What's the biggest couch you can slide around a 90-degree corner? Hosted by: Michael Aranda

It's taken the work of many programmers to turn computers into something we carry in our pockets, and here are five (technically 10!) that we think you should be aware of.

The equator is a clear and accurate line around Earth that makes measuring latitude a precise science, but when it came to figuring out how to do that with longitude, British sailors were at a loss. Until they devised a competition....

Hundreds of years ago, your ancestor stole a magical tarot deck from Fate herself— and it came with a terrible cost. Once every 23 years, one member of your family must face Fate in a duel with rules only known to your opponent. And...

Jessi and Sam the Bat team up to answer your questions about space, like: How was the universe created?

By 1917, Albert Einstein had explained the relationship between space and time. But, that year, he designed a flawed airplane wing. His attempt was based on an incomplete theory of how flight works. Indeed, insufficient and inaccurate...

The fabled Mirzakhani wand is the most powerful magical item ever created. And that's why the evil wizard Moldevort is planning to use it to conquer the world. You and Drumbledrore have finally discovered its hiding place in a cave, but...

A few years ago, the king decided your life would be forfeit unless you tripled the gold coins in his treasury. Fortunately, a strange little man appeared and magically performed the feat. Unfortunately, you promised him your first-born...

Eigenvalues and eigenvectors are one of the most important ideas in linear algebra, but what on earth are they?

Eigenvalues and eigenvectors are one of the most important ideas in linear algebra, but what on earth are they?

What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.

What is integration? Why is it computed as the opposite of differentiation? What is the fundamental theorem of calculus?

An introduction to group theory, and the monster group.

What is the derivative of a^x? Why is e^x its own derivative? This video shows how to think about the rule for differentiating exponential functions.

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.

Introduction to the derivatives of polynomial terms and trigonometric functions thought about geometrically and intuitively. The goal is for these formulas to feel like something the student could have discovered, rather than something...

How to think of 3x3 matrices as transforming 3d space

An introduction to the quantum behavior of light, specifically the polarization of light. The emphasis is on how many ideas that seem "quantumly weird" are actually just wave mechanics, applicable in a lot of classical physics.

What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.

An overview of what calculus is all about, with an emphasis on making it seem like something students could discover for themselves. The central example is that of rediscovering the formula for a circle's area, and how this is an...

A method for thinking about high-dimensional spheres, introduced in the context of a classic example involving a high-dimensional sphere inside a high-dimensional box.

In which John Green talks about the methods of writing history by looking at some of the ways that history has been written about the rise of the West. But first he has to tell you what the West is. And then he has to explain the Rise of...

What is the derivative of a^x? Why is e^x its own derivative? This video shows how to think about the rule for differentiating exponential functions.