On earth it rains water, on the exoplanet WASP-76b, it rains liquid iron, but no matter what planet you're on, the rain drops there have a lot more in common than you might think.

How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?

One of the top chefs from Pasta Palace has been kidnapped by operatives from Burger Bazaar hoping to learn the location of their secret sauce recipe. Little do they know that a third party— Sausage Saloon— has sent you, their top spy, to...

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

Some foundational ideas in linear algebra: Span, linear combinations, and linear dependence.

Medical animator David Bolinsky presents 3 minutes of stunning animation that show the bustling life inside a cell.

How Long To Fall Through the Earth?

What is the Riemann zeta function? What is analytic continuation? This video lays out the complex analysis needed to answer these questions.

Logarithms are confusing, but perhaps some alternate notation could make them more intuitive.

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

You've promised to get your son the cutest creature in creation: the cuddly. It's part of the Wuddly species, cousin to the terrifying duddly and the hideous fuddly. To make one, 100 eggs are placed in an incubator to undergo egg fusion,...

How counting in Ternary can solve a variant of the Tower's of Hanoi puzzle, and how this gives rise to a beautiful connection to Sierpinski's triangle.

Your friendly local weather person says there's a 10% chance it will rain today, so you throw on your flip-flops and head out to enjoy a beautiful day. Next thing you know, you're running through puddles, trying to get out of a...

What is the Riemann zeta function? What is analytic continuation? This video lays out the complex analysis needed to answer these questions.

What are limits? How are they defined? How are they used to define the derivative? What is L'Hospital's rule?

As Numberland's best detective, you thought you'd seen it all. But the desiccated corpses of prominent natural numbers have been showing up all over the city. A lockdown is ordered from sundown to sunrise, and it's still not enough to...

The underworld is overcrowded, and Zeus has ordered Hades to let some spirits out. Hades arranges all the souls of the dead in a line before Cerberus. When one of his three heads bites down on the soul in front of it, they'll get...

How to think about matrix multiplication visually as successively applying two different linear transformations.

When you think of matrices as transforming space, rather than as grids of numbers, so much of linear algebra starts to make sense.

Do animals think? It's a question that has intrigued scientists for thousands of years, inspiring them to come up with different methods and criteria to measure the intelligence of animals. Bryan B Rasmussen navigates through this...

Two proofs for the surface area of a sphere

How to think about implicit differentiation in terms of functions with multiple inputs, and tiny nudges to those inputs.

Origami, which literally translates to "folding paper," is a Japanese practice dating back to at least the 17th century. In origami, a single, traditionally square sheet of paper can be transformed into almost any shape, purely by...

On their 20th birthday, identical twin astronauts volunteer for an experiment. Terra will remain on Earth, while Stella will board a spaceship. Stella's ship will travel to visit a star that is 10 light-years away, then return to Earth....