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.

What happens when you divide things that aren't numbers?

In this video Paul Andersen explains how atoms are conserved in a chemical reaction. This can be seen in a chemical equation where the subscripts represent the atoms in the molecule and the coefficients represent the molecules. The...

Moser's circle problem, and its solution.

Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?

A solution to the puzzle involving two blocks, sliding fricionlessly, where the number of collisions mysteriously computes pi

Classical computers struggle to crack modern encryption. But quantum computers using Shor's Algorithm make short work of RSA cryptography. Find out how.

So we ended the last episode nearing the close of the 1980s and Nintendo had become the dominant player in the home console market, but Sega, originally a slot machine game company during World War 2, was looking to get its own console...

A solution to the puzzle involving two blocks, sliding fricionlessly, where the number of collisions mysteriously computes pi

A solution to the puzzle involving two blocks, sliding fricionlessly, where the number of collisions mysteriously computes pi

Paul Andersen explains how to use mathematics appropriately. He begins by emphasizing the important role that mathematics plays in the life sciences today and in that the future. He describes important mathematical equations in each of...

Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?

A new drug reduces the risk of heart attacks by 40%. Shark attacks are up by a factor of two. Drinking a liter of soda per day doubles your chance of developing cancer. These are all examples of a common way risk is presented in news...

An animated introduction to the Fourier Transform, winding graphs around circles.

TED curator Chris Anderson shares his obsession with questions that no one (yet) knows the answers to. A short intro leads into two questions: Why can't we see evidence of alien life? And how many universes are there?

What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.

Your body is really good at keeping its temperature at around 37� C, but have you ever wondered why?

In this episode of Crash Course Psychology, Hank takes a look at WAIS and WISC intelligence tests and how bias can really skew both results and the usefulness of those results.
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An algorithm for solving continuous 2d equations using winding numbers.

What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.

An algorithm for numerically solving certain 2d equations. Even though we described how winding numbers can be used to solve 2d equations at a high level, it's worth pointing out that there are a few details missing for if you wanted to...

Is the Universe Entirely Mathematical feat. Max Tegmark

More than a billion people worldwide, mostly children, do not have a legal identity. In many countries, this means they can't get access to vital services like health care and education, says legal identity expert Kristen Wenz. She...