S^2 isn't a special case though: Brouwer's showed the theorem can be easily extended to high dimensions, hence today we usually consider the more general statement that there is a nonzero tangent vector field on the n-sphere S^n iff n is odd.
Not only does it generalize to higher n, it also shows a bit more: not only that the lack of such vector field for an even n, but the also the existence of such for odds.
SegfaultSeagull · 1h ago
I majored in mathematics and remember encountering this theorem in a topology course. I giggled then, and 20 years later I giggle again.
cool_dude85 · 6m ago
Much more niche than the hairy ball theorem is the Cox-Zucker Machine, supposedly they decided during the first year of undergrad that they eventually had to work together.
hinkley · 1h ago
Have you considered a job in Defense? They love acronyms you can’t say out loud.
xanderlewis · 1h ago
In German it’s called the Hedgehog Theorem.
Clearly, what they say about Germans is true.
gerdesj · 50m ago
Ooh go on, what do they say about Germans?
I lived in West Germany for some years back in the day and I don't recall the locals being too shy. Frankly the Germans and the Dutch seemed to have had a rather more ribald sense of humour than the "oo err Missus" efforts we Brits fielded back then.
To be fair we could robustly swear on telly after 2100, provided it didn't involve too many rude bits and you could not misspell one variant of King Canute's name or Matron would be jolly upset.
Anyway, I'm pretty sure someone called this the "dog's arse" (it has to go somewhere!)
fxwin · 58m ago
Also known as the Combed Hedgehog Theorem (which i like a bit better)
orlandpm · 27m ago
Heard a mathematician friend call this the “hairy sphere theorem” once. At first I thought he was being a prude, but now I appreciate that the theorem is about spheres, as opposed to balls.
Not only does it generalize to higher n, it also shows a bit more: not only that the lack of such vector field for an even n, but the also the existence of such for odds.
Clearly, what they say about Germans is true.
I lived in West Germany for some years back in the day and I don't recall the locals being too shy. Frankly the Germans and the Dutch seemed to have had a rather more ribald sense of humour than the "oo err Missus" efforts we Brits fielded back then.
To be fair we could robustly swear on telly after 2100, provided it didn't involve too many rude bits and you could not misspell one variant of King Canute's name or Matron would be jolly upset.
Anyway, I'm pretty sure someone called this the "dog's arse" (it has to go somewhere!)