My experience with HN is, there are some very thoughtful mathematicians engaging in deep research around here. Some of the posts here may make no sense to 99% of the readers ("why on earth should I care about 7-dim stuff, I just don't give a damn"), but it may just be the lightning strike needed for someone to make important breakthrough in certain area of mathematics.
This property of 3/7 dimensional cross product is not terribly insightful. It's taught to undergrads. It's not really a hallmark of advanced mathematical research.
