How do you think about a non-square matrix as a transformation?

You've come a long way to compete in the great Diskymon league and prove yourself a Diskymon master. Now that you've made it to the finals, you're up against some tough competition. In round one, you'll face a single opponent and get to...

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

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

Jupiter's storms cover the planet, but the ones at the planet’s poles have mystified astronomers for years: why haven’t they merged together yet?

This is an absolutely beautiful piece of math. It shows how certain ideas from topology, such as the mobius strip, can be used to solve a slightly softer form of an unsolved problem in geometry.

Two proofs for the surface area of a sphere

Today we’re going to talk about numeracy - that is understanding numbers. From really really big numbers to really small numbers, it's difficult to comprehend information at this scale, but these are often the types of numbers we see...

A beautiful proof of why slicing a cone gives an ellipse.

Hidden truths permeate our world; they're inaccessible to our senses, but math allows us to go beyond our intuition to uncover their mysteries. In this survey of mathematical breakthroughs, Fields Medal winner Cedric Villani speaks to...

Quantum mechanics is weird and seems a bit...complicated. But understanding it can help us to understand the universe.

Today is the anniversary of the best-worst day of your life. The best part was discovering a subterranean city on Mars. The worst part was when you lost contact with Earth. You and the other 99 scientists have spent the year engineering...

Drawing curves that fill all of space, and a philosophical take on why mathematics about infinite objects can still be useful in finite contexts.

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...

A curious pattern in polar plots with prime numbers, together with discussion of Dirichlet's theorem

Once a year, thousands of logicians descend into the desert for Learning Man. At the center of that gathering is the world's most exclusive club, where under the full moon the annual logician's rave takes place. The entry is guarded by...

Have you ever sat down to take a math test and immediately felt your heart beat faster and your palms start to sweat? This is called math anxiety, and if it happens to you, you're not alone: Researchers think about 20 percent of the...

When a piece of cryptography is described as having "256-bit security", what exactly does that mean? Just how big is the number 2^256?

An overview of backpropagation, the algorithm behind how neural networks learn.

A visual for derivatives which generalizes more nicely to topics beyond calculus.

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

The determinant has a very natural visual intuition, even though it's formula can make it seem more complicated than it really is.

A brief intro to the current theory of (almost) everything - the Standard Model of particle physics. It's like cake, only universal.

Your friend's birthday is tomorrow, and he's turning... well... you've forgotten. A ginormous cake has been prepared and your job is to sculpt his age as the chocolate centerpiece. The birthday boy is a giant, and you're afraid that if...