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...

People love eating pizza, but every style of pie has a different consistency. If "New York-style"--thin, flat, and large--is your texture of choice, then you've probably eaten a slice that was as messy as it was delicious. Colm Kelleher...

An overview of what a neural network is, introduced in the context of recognizing hand-written digits.

Happy pi day! Did you know that in some of his notes, Euler used the symbol pi to represent 6.28..., before the more familiar 3.14... took off as a standard?

In a lively show, mathemagician Arthur Benjamin races a team of calculators to figure out 3-digit squares, solves another massive mental equation and guesses a few birthdays. How does he do it? He’ll tell you.

Bad news: your worst enemies are at the gate. Your fledgling kingdom guards the world's only herd of tiny dino creatures. To you, they're sacred. To everyone else, they're food. The three closest nation-states have teamed up to smash...

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

Web cartoonist Randall Munroe answers simple what-if questions ("what if you hit a baseball moving at the speed of light?") using math, physics, logic and deadpan humor. In this charming talk, a reader's question about Google's data...

The Heisenberg Uncertainty Principle might not mean what you think it means: Hank clears things up for us in this edition of IDTIMWYTIM, by distinguishing between the Uncertainty Principle and the Observer Effect, which are often conflated.

What is a vector? Is it an arrow in space? A list of numbers?

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

Microsoft's Stephen Lawler gives a whirlwind tour of Virtual Earth, moving up, down and through its hyper-real cityscapes with dazzlingly fluidity, a remarkable feat that requires staggering amounts of data to bring into focus.

SETI researcher Seth Shostak bets that we will find extraterrestrial life in the next twenty-four years, or he'll buy you a cup of coffee. He explains why new technologies and the laws of probability make the breakthrough so likely --...

Today we’ll explore the history of education as a social institution, with a specific focus on how the US organizes its educational system. We’ll look at education through the lenses of some sociological paradigms: structural...

The math of backpropagation, the algorithm by which neural networks learn.

As earth temperatures continue to rise, what's really to blame?

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

A very clever proof of Euler's characteristic formula using spanning trees.

Mathematician Steven Strogatz shows how flocks of creatures (like birds, fireflies and fish) manage to synchronize and act as a unit -- when no one's giving orders. The powerful tendency extends into the realm of objects, too.

There are a few special right triangles many of us learn about in school, like the 3-4-5 triangle or the 5-12-13 triangle. Is there a way to understand all triplets of numbers (a, b, c) that satisfy a^2 + b^2 = c^2? There is! And it uses...

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

Michael Moschen puts on a quietly mesmerizing show of juggling. Don't think juggling is an art? You might just change your mind after watching Moschen in motion.

What kinds of tools do astronomers use to calculate the age of the universe, and how can they determine the speed of its expansion?

Think you're good at guessing stats? Guess again. Whether we consider ourselves math people or not, our ability to understand and work with numbers is terribly limited, says data visualization expert Alan Smith. In this delightful talk,...