This is a really fun video by 3Blue1Brown about the cleverness and elegance of Hamming codes, simple algorithms that help recover data when some of it gets mangled – for example, if you scratch your CD disc:

The default assumption for complete data protection might be to have a second, backup copy to be sure. But Hamming codes not only promise the same kind of safety in a fraction of the space needed – they also can point to where exactly the data was damaged, and in many cases they can even fix the damage, for free. And the code required is trivial, too.

It reminded me quite a bit of this video about Unicode, another example of beautiful and smart encoding.