The Numerphile video has been debunked by everyone else in the math-popularization community: http://blogs.scientificamerican.com/roots-of-unity/does-123-really

The Numerphile video has been debunked by everyone else in the math-popularization community: http://blogs.scientificamerican.com/roots-of-unity/does-123-really-equal-112/ http://blogs.scientificamerican.com/roots-of-unity/does-123-... (and also see discussion of that article on HN The "-1/12" "mystery" is well settled math (but mathematicians are always looking for more elegant or general perspectives on things), and (standard-issue) sloppy notation in physics. The only "mystery" is why people who should know better intentionally use incorrect terminology to dazzle lay-people, creating a mystery where there is none.