Numberphile

There are many YouTube channels featuring and explaining math, such as Mathologer and
MindYourDecisions, but by far the best that I’ve been able to find is Numberphile. They generally do a good job explaining the derivation of their theorems, but even when they don’t they are valuable for the wonder they induce and for the small tidbits of knowledge that can be combined with facts heard elsewhere to build up a more complete picture of things. It’s fascinating. Many times I have gone online just to watch one or two videos and ended up staying up all night.

Why are there infinite magic squares and only two magic hexagons? What is the longest possible game of tree? What are the spooky connections between the parts of the triangle? How can the same equation lead to such simple order and such complex chaos by only slightly changing one variable? What is a strange attractor? Can we find the digits of pi hiding in the Mandelbrot set? Can we find the Fibonacci sequence hiding in the Mandelbrot set? Why is 41 special?