How does bitcoin work? What is a "block chain"? What problem is this system trying to solve, and how does it use the tools of cryptography to do so?

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

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

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

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

A classic puzzle in graph theory, the "Utilities problem", a description of why it is unsolvable on a plane, and how it becomes solvable on surfaces with a different topology.

How couting in binary can solve the famous tower's of hanoi problem.

Divergence, curl, and their relation to fluid flow and electromagnetism

A geometry/probability question on the Putnam, a famously hard test, about a random tetrahedron in a sphere. This offers an opportunity not just for a lesson about the problem, but about problem-solving tactics in general.

Why do chickens and turkeys have white meat and dark meat? And, like, gross, but .. do humans have the same thing? It's all about our muscles: what they're made of, and what they're made for. Quick Questions has the answers!

Dr. Scott Mills joins Hank to talk about studying color changing fur and evolutionary conservation. Scott and graduate student Lindsey Barnard bring a snowshoe hare and Jessi from Animal Wonders brings two Netherland Dwarf rabbits.

Problem 2 from the 2011 IMO

A beutiful derivation of a formula for pi. At first, 1-1/3+1/5-1/7+1/9-.... seems unrelated to circles, but in fact there is a circle hiding here, as well as some interesting facts about prime numbers in the context of complex numbers.

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.

To freshen up your Apollo knowledge, here is a good dive into the science and engineering that put people on the moon.

Paralyzed by a stroke, Henry Evans uses a telepresence robot to take the stage and show how new robotics, tweaked and personalized by a group called Robots for Humanity, help him live his life to the full. He shows off a nimble little...

Poop: it's gross... it's funny... it's educational?! Join Jessi and learn all about how you can observe poop in your neighborhood to figure out what kinds of animals live near you! Just don't touch it!

Problem 2 from the 2011 IMO

We all know that brushing our teeth is important but now with this experiment you can actually SEE how brushing keeps your teeth clean!

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.

What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.

Brown cats are something of a rarity, but you may have something pretty close.

A beautiful solution to the Basel Problem (1+1/4+1/9+1/16+...) using Euclidian geometry. Unlike many more common proofs, this one makes it very clear why pi is involved in the answer.

Since eye color is determined by chemical and structural differences in the eye, it seems logical that different eye colors see the world in different ways.