Here's a pair of blog posts explaining the math behind the "Rolling Shutter Effect": Playing Detective with Rolling Shutter Photos and Rolling Shutters.
Can you ever be reasonably sure that something is random, in the same sense you can be reasonably sure something is not random (for example, because it consists of endless nines)? Even if a sequence looked random, how could you ever rule out the possibility that it had a hidden deterministic pattern? And what exactly do we mean by “random,” anyway?
1 + 2 + 3 + 4 + 5 ... = -1/12 -- Numberphile explains a counter-intuitive summation of an infinite series. [more inside]
How To Fold a Julia Fractal. A beautiful interactive introduction to complex numbers, fractals and waves. (Requires WebGL). To Infinity And Beyond is a similar introduction to calculus.
Old Theories As Limits of New Ones -- Theoretical physicist, Lubos Motl, takes a brief tour through the history of physics, and explains the simple mathematical relationship of old theories to the theories that replace them.
Horizon asks "What is reality?" -- youtube for links for those outside the UK: 1, 2, 3, 4. It's a hard question. To help you answer it, Stanford has a set of free courses available on line by Leonard Susskind: General Relativity, Cosmology, New Revolutions in Particle Physics, Quantum Entanglement, Special Relativity, Classical Mechanics, Statistical Mechanics, The Standard Model. (Each link is to lecture 1 of a full college course of a dozen or so lectures.) If you need help with the math, the Khan Academy should help get you up to speed.
Music is Math (lots of different variations on the page. Watch this one in full screen and with headphones.)