The product rule and chain rule in calculus can feel like they were pulled out of thin air, but is there an intuitive way to think about them?

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

What is a change of basis, and how do you do it?

Taylor series are extremely useful in engineering and math, but what are they? This video shows why they're useful, and how to make sense of the formula.

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.

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.

What is a change of basis, and how do you do it?

What exactly are fractals? A common misconception is that they are shapes which look exactly like themselves when you zoom in. In fact, the definition has something to do with the idea of "fractal dimension".

The third and final part of the block collision sequence.

* Viewer discretion advised. This video includes discussion of mature topics and may be inappropriate for some audiences. Physics and marketing don't seem to have much in common, but Dan Cobley is passionate about both. He brings these...

What exactly are fractals? A common misconception is that they are shapes which look exactly like themselves when you zoom in. In fact, the definition has something to do with the idea of "fractal dimension".

The product rule and chain rule in calculus can feel like they were pulled out of thin air, but is there an intuitive way to think about them?

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...

In 2009, researchers ran a simple experiment. They took everything we know about our solar system and calculated where every planet would be up to 5 billion years in the future. They ran over 2,000 simulations, and the astonishing...

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

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.

A classic problem that Johann Bernoulli posed to famous mathematicians of his time, such as Newton, and how Bernoulli found an incredibly clever solution using properties of light.

An introduction to what a derivative is, and how it formalizes an otherwise paradoxical idea.

The product rule and chain rule in calculus can feel like they were pulled out of thin air, but is there an intuitive way to think about them?

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

The cross product is a way to multiple to vectors in 3d. This video shows how to visualize what it means.