That video was one of the best videos on mathematics I have ever seen; the visualizations to aid in the explanation of Newton's "new" algorithm were absolutely top-notch. I'm not sure I could have followed it without them. With them, I feel like I know it well enough now to explain it to someone else.

The thing with applied cryptography is that everyone is expecting the attacks to get better over time, sometimes in big and inconvenient bursts. There are several strategies to mitigate this, including oversizing security margins by a certain amount (so that an innovation that improves an attack by an order of magnitude or two isn't an instantaneous shattering of your whole security model), and having what's sometimes termed "algorithm agility" (which has somewhat fallen out of favor recently due to having its own class of bugs due to the implementations around, say, an optional NONE pluggable cipher type).